Regardless of whether you ask her to go to shopping (indirect) or directly for a date, your "rep" can be affected by the gossiping. You ask her to go shopping, the chicks arent going to be stupid and think you're not trying to spend time with them for a romantic reason, unless you have a rep of a guy who goes shopping with everyone. Any excuse, is gonna be seen as you have another motive, unless you really have that social shopping guy vibe. So I wont recommend shopping excuse as chicks will talk regardless. Chicks may just wonder what it really means, lets say they give you the benefit of the doubt, but then you're battling uphill and dont even know if the chick is interested when you meet to shop.

Now if you go direct route, and ask the chicks you're attracted to, go ahead. If you dont care about your rep and have solid enough "game." If you're seen as the attractive charming guy at the class, asking out a bunch and hitting and missing their gets you the player vibe, which aint bad. If you're the weird lame guy, asking out a bunch gets you the creepy guy vibe which is bad.

Personally, I'd be a bit more discreet if the gossip is that heavy; I'd flirt with all the chicks, be cool with guys, mingle, have fun and read signals. Start the competition vibe as Jack said. Flirt with Sally, flirt with Betty, flirt with Susie, talk to Joe, dance with the old chick, oh sally is talking about she's hungry? lets grab some food. bang. Go back next class, flirt around some more, betty seems down, hey lets go out this weekend, bang. Or maybe she says I have a bf. Cool. Flirt some more bounce around. Hey let a group of us move to the club after class one night. Roll in their with some guys and girls. Dance, meet some other chicks at the club. Flirt some more. 200 people is alot to deal with, so you should be dynamic.

This is just the OP looking for counter measures before the situation even demands them.

50$ he will end up doing nothing.

_________________
I know my place. It's me on top of the world.

My in depth texting & dating guide.
There's no such thing as shit-tests.
How to keep a girl.

You are not as cool as you think you are. Haha. You're a guy with 3800+ posts on a pickup forum who appears in EVERY thread with your try-hard snarky posts that add nothing to the discussion except try to make OPs - ppl looking for advice - feel inadequate. But it's cool bro, keep posting. I'm sure you got the most exciting life to have all this time to post in this forum lol. I bet when you're not banging all the hoes you're really busy doing other stuff.

YOU'RE AWESOME!!!!

Being judgemental will take you far in your relationships

I'm not on this forum to tender your feelings. But the fact that you take my statement personal reflects that it may have had some accuracy to it.
The purpose of this place is to help people improve. If you feel inadequate, that's because you are. And that's fine, it's why you're here.
I don't sugar coat my advice. When I see someone acting stupid I call it for what it is. If tough love does fare well with you, that's cool, but if you truly want to become better, a good place to start is by leaving your ego at the door. Often times it's a guy's biggest enemy.

_________________
I know my place. It's me on top of the world.

My in depth texting & dating guide.
There's no such thing as shit-tests.
How to keep a girl.

I don't understand why so many in these forums call down guys asking for advice

I don’t have a problem w helping each identify problems with each other's games. I just fail to see what "name calling" and personalized attacks do for anyone

It's weak, it's petty, it's insecure… it's the epitome of "beta male" behaviour

GIVE VALUE to one another guys. Demonstrate you are "The Alpha" and help your brothers who are struggling. We're all here because we accept we need help with women.

I have some familiarity w salsa groups.

You could try the "isolate and seduce" approach but it implies you're ashamed of what you're doing. Women want men to own their sexuality and interest in the opposite sex. They know what you're doing by trying to isolate them already. Hitting on a girl in front of her friends is both risky but also potentially very rewarding because you are taking the risk of being rejected and giving her value by taking that risk but bear in mind she can't risk succumbing to a weak approach because it will lower her value to her friends. The "isolate and seduce" strategy projects one's shame over issues of sexuality. They will sense you're underlying shame and will be far more likely to disqualify you because of it

Instead try this: BUILD UP YOUR SOCIAL VALUE IN THE GROUP.

Dance with greater passion. You don't have to become a "great dancer" just genuinely enjoy what you're doing. In fact NOT being a great dancer (but still being a competent dancer) can be a "cool vulnerability" that can make you more relatable and increase their comfort levels with you. If you genuinely feel good dancing the girls will feel and want to have some of that for themselves.

Sport a warm, comforting, "self-entertained" smile especially when you're dancing. Correct your body language issues especially when "asking" for a dance. Do not orient your feet, hips and shoulders to her. I made that mistake once: I got shot down twice in quick succession at a dance doing that. Instead, orient your feet, hips and shoulders perpendicular to her feet/hips/shoulders and extend one hand to her (open, palm up) and lean on your foot furthest from so as to imply your about "go somewhere" and do something "more interesting" than what she's doing right now (i.e., standing there doing nothing) and you're inviting her to come along. I didn't get shot down again that night.

Be fun. Laugh at your mistakes. Be "oblivious" to others mistakes. Let them sense how good dancing makes you feel and in turn they will feel good too.

Volunteer more within the group to help out. The organizers are always needing help with something. I volunteered to bartend at our group's annual Salsa Night. Holy shit some of the girls were eye fucking me like crazy that night.

Get to know everyone in the group (especially the core members): likes & dislikes, interests, hobbies… where they live, where they work, where they coffee, how they get around << these are logistics issues boys: pay close attention.

Don't just pay attention to the hot girls. Flirt and have fun with everyone. Give everyone attention BUT develop your capacity for spiking people's emotional interests AND THEN leaving them on a high note. It's called "breaking rapport" and is a powerful way of projecting the polar opposite of neediness. It's devastatingly attractive.

Paralinguistics are important: reduce your use of "I", use more "you" and "us / we vs them". It demonstrates you're "outwardly" focussed and implies you're secure in who you are that you don't have to draw attention to yourself for validation but rather you're interested in other people.

Always have something to do after the weekly salsa thing that you can go to (preferably something real and fun that plays to your strengths) that you can mention you're going to do. Mention the stuff you've been doing the previous few days to show you're a busy man and you've got more to do. You're a man in motion.

When you've demonstrated more value to the group like this (and there are more watts too) they will not only expect you to exercise your social options among the girls in the group… they will accept it and even encourage it.

Jealousies may develop. Good. It will cultivate competition for your masculinity. DO NOT BE ASHAMED OF IT.

Be discrete, of course. Running your mouth off about your conquests in the group will be far worse for your reputation than approaching multiple girls at your salsa group. The girls want you to be discrete. The "mystery" that you create over "did they hook up?" and how cool you are about it will make other girls in the group value you even more and will be more willing for you to enjoy them physically because they know you can keep a secret.

It may require more work. A lot more work but the potential rewards to you if you can pull this off can be enormous and certainly worth pursuing.

...and there will be far less risk of rejection in the end.