Some hints are obvious, as in my case, others seem more subtle as the other blokes have mentioned. I would err on the side of them just being nice and having some trust in you, and enjoying your company rather than leaping to the belief that she wants a real date. This can be a tough gig. She might be holed up in her hotel all day, and finds a client who seems nice and fun to talk to -and someone whom she can talk freely about this industry, which she likely can't to others - so maybe she's hungry or needs a coffee so she invites you along. (If you join her of course be a gentleman and pay for you both). I've had that happen half a dozen -10 times or so but i am under no illusion she wants to date for real. Instead i presume that she has confidence that i not only know "the line" but that i also won't cross it (i.e., believe she's somehow falling for me lol or that I really have any chance with her). Thus she can let her guard down a bit knowing her signals won't be misinterpreted.
If she really wants to hang out, then if she says something like that just ask "what do you have in mind?". Then read her signals. Don't be afraid to ask for the details, just let her know you enjoy her company and don't want to misinterpret anything. I can imagine some client once thought the hangout offer was great and then she cited her social rates lol. Don't be that guy. Thus assume professional until she says otherwise. Rather be in the position of "so what's your rate on this proposed dinner date"? Versus "oh, sorry, I thought this was a personal invite, I didn't know this was business and you were charging your time...uh, let me find an ATM...."