Is this a good way to do it? There's this woman who has shown indicators of interest but I only see her when she is with her friends.

I'm thinking of asking her out in front of everybody. I would start by saying hello to everyone in the group. After some small talk, I'd say to the target: "You know (first name), you seem like you could be an interesting person, but I have little to base you on. Would you like to converse with me over tea?"

If she says no or doesn't make concrete plans, then I'd say "It's your call, I bid you all fair tidings."

If she says yes I'd hand her my business card and instruct her to text me her number if we can't go for tea right then and there.

Comments? Am I on the right track or should I scrap this idea completely and start over?

Why don't you isolate her ? Maybe she would want to say yes but the social pressure would make her say no.