Oh man I know exactly where you're coming from, I still find I have that same problem from time to time. Day game can be a challenge sometimes with this but I have to tell you that the best advice I can give in one sentence is that it comes with practice, eventually you will get a feel for it and soon enough you'll realize you're a lot better than when you first started. Practice as much as you can
I like your idea to have them come with you, give it a try and see where it goes. Personally I'd throw in more conversation beforehand though. Maybe something like
Me: Hey! You guys walk around looking like you own the place. We have no map, and no idea how to find ____ roller coaster but we heard it's AWESOME. Any ideas?
Set: Haha yes we own it(i donno random girl bs response haha) yeah you can go blah blah blah.
M: Alright, sounds good. You guys must come here often to know your way around!
Set: Yeah we've been here like, a hundred times
M: Wow, so I bet you'd consider yourselves pretty adventurous then huh? I bet you are total troublemakers too!
S: *laugh* yeah we're the most adventurous ones here but we aren't troublemakers!
M: Yeah I can feel it, I just get that vibe you're probably plotting some master plan right now. I bet you gave us wrong directions so you can all laugh maniacally when me and my friends skip off in the wrong direction!
S: Yes we're evil geniuses.
M: Okay evil geniuses, give me your best villain laugh! Pretend like you just hatched your evil plan on the world. (donno, this actually sounds funny, might use this tonight haha. I made this up as a variation on telling a girl to give you her best animal noise or dance move when she asks for a cigarette).
S: *evil laughs*
M: I wasn't sure about you girls before, but you're alright. Ok my "so-called" adventurous girls, let's head over to that badass rollercoaster I asked about earlier. My friends and I are making today a party, you should join us.
There's a thousand different ways you can take a conversation, I just made up their responses(obviously favorable ones) and used a lot of things to get them to qualify and laugh. It's going to be different for each and every set you open, so just have fun with it. Just be high energy and show them how fun you are. Follow it up just like you said by trying to get them to bounce to a ride or whatever it is you're "looking for" and enjoy your new instant dates! haha.
Also, something I focused too much on when I was just starting out was the outcome. I thought I had to close every single set, and that attitude ended up being detrimental to my performance and even took a toll on how much fun I had because I was preoccupied with an outcome. Just have a good time, get some practice in, and if an interaction is going really well, give closing a shot. Hope this helped you out!