I'm sure drink time is off the clock, but of course, you'll pay for drinks &  hors d'oeuvres.

Sometimes it is OTC, sometimes on, and sometimes in between.

Each case is different.

If bar time is on the clock & you spend 3 hours at the bar, you'll have to cough up bucks for 4 hours of her time.  I'd suggest saying "I'd love to take you out for drinks.  That time is off the clock correct"???

A smooth way to come out and say it to say something like:  I'd hate to take advantage of your time.

If she then says something like:  Oh, don't worry about it, we're just having a friendly time together; then I guess that means OTC.

About a month ago I saw a provider for the first time. It was a good time for all. A week ago she emailed letting me know she was in town. Due to work, I was unable to make an appointment. She asked after the next appointment "maybe go out and grab a drink after". I just wanted to know what others think about this. Is it off the clock or on the clock?

I've never really booked a "dinner date" with a lady.  But often after a session if I feel the chemistry thing with a babe and I'm gonna have a drink or bite to eat before heading home or calling it an evening if it is an outcall situation I might invite her to join me.  Also, it is not unusual for a fave or two of mine to contact me to hook up for a drink or two when they close up shop for the day.  I never have expectations beyond time booked for a session , but there can be a social element to the hobby.    It really sounds like to me you are being invited to simply grab a drink.  A good response might be " "sure , but only if it's my treat".    Have fun.

or else... or else... I guess I'll compensate her if she has a problem with it. lol

Seriously though, I don't particularly enjoy paying a girl just to watch her drink beer and yap.  
If she's the one asking, then she better damn well not expect me to compensate her for her time.  
Got plenty of female friends to go out with if I just wanted to watch them drink and eat...

( If once in a blue moon I see a hot babe and I decide to swallow my pride, paying her for her time...  then she better put on the full GFE hollywood show. She better be making me feel like the king of the world, instead of making me listen to her problems and shit, lol )

On the clock or off the clock, I have no problem buying the lady (and myself) a very nice round of drinks though but it would be nice if she knows how to drive a stick shift (no, not that kind of stick, lol)  so she can drive me back home. Even better if she takes me back to her place and let me sleep in her bed with her, OTC. Hope she doesn't mind waking up to a puddle of puke though.  lmao

Also no rule that drinks are always on the man (civie or not). If you have to buy a woman something to spend time you are on the clock imho.  Better to draw the line and know where you stand, thats just me.

Had an amazing session with a true carnivore.  We were spent.  She'd said earlier I was her last session.  Then she said she was starving.  I said, "Let's go get some dinner on me, just friends."  She said, "Great."  She didn't even pick an expensive place.  We had a great dinner, not expensive and I enjoyed the hell out of it.

off the clock... I tend to like to meet gents in the bar first to give it a "date" feel... also then I can get their mind racing as I flirt with them... it is totally OFF the clock!

I know a provider that says stuff like that all the time. But it is always next time. I think she just wants to tease me into haveing a next time. I keep seeing her because she is a beter fuck than any other provider I have seen