Oke, sounds good.
Now lets analyse:
You want to hook up with a ex-girlfriend, that wanted to take things slow, she felt you was getting needy and things cooled off completely. Now you want the once in a while hook up established in a casual social environment with a few hours to work with.
I will not bullsht you, this is a difficult situation and falling is quite likely. So clear your mind and convince yourself you're only going there to meet a friend and have a nice time. This state of mind is really important, it will help you to come across cool, relaxed and confident. This will act as a damage control to the needy signs from a while back.
Please fill in the parts in the situation that I don't yet have info on, since it's important how your situation is.
Oke ready?? Here it comes:
[Step 1 - Prepping]
The obvious basics are presentation: make sure you look your best and feel awesome. So no unhealthy stuff that could cause any acne whatsoever and start/continue exercising just to feel more energetic and pumped up.
Wear whatever fits your body and style, your preference and especially HER preference best. You said it was a business meeting right?? So then I would assume SUIT-Up, all women love suits, BUT MAKE sure it fits perfectly, bad fitting suits look clumsy and boy-ish.
If the situation does not require a suit and you don't think you can come up with a nice style to catch her fancy, just make up a business meeting AFTER the "date", not before. This will allow you to meet have lunch or whatever, quick exit and have a drink (night time) before you leave (but you're not leaving, until the next day

).
This all changes if she doesn't like suits off-course.
[Step 2 - Reading the situation]
You know her better than me, so watch carefully. She is likely to expect you to fall in the pattern that you had before (being needy). So if she dresses to impress (A) you're in and she is hoping to catch your fancy if not (B) she wants to make a statement that there will be no hooking up. Either way you can turn things around.
A) She care what you think about her, but don't get to greedy because most girls like to see exes drool . You can flirt with her but keep it casual. Your profile should be (being charismatic and charming but not really showing any intention of wanting to sleep with her. Pay her the obvious complements and then steer away from the topic immediately.
B) More complicated. She wants to make a point and you need to change her mind. This mean have tons of fun, do not pay her any compliment, make her laugh, and just have a really fun time. This will spark new interest and cause the shift and will allow you to meet up later for the drink. Make a few back handed comments (or the well known negs, but keep it nice).
PS: This strategy has a big chance of ending up in the friend zone, however your situation is just that difficult. But you know what they say, high risk equals high reward.
The most important part about your situation lies in the first 5 sec, that's why your presentation will be so important. If you're comfortable enough with lying convincingly, text her that you will be 5 min late had to do 'something' then show up 10 min late. If this was something she complained over during the relationship (you always showing up late , DON'T do this) be earlier and have a coffee black (espresso)
If she wants the hook up all you have to do is real her in, she wants this otherwise she will back down. If she doesn't want the hook up you need to go the opposite way and show her how awesome you are and that you are not interested in the hook up.
If step 1 and 2 are successful you don't need step 3 and 4 just go with the flow. If not, go safe a baby or something because you need a miracle.
I'm gone stop know because it's becoming too lengthy, however I want to advice you as good as possible but picking-up/hooking up/dating/relationships whatever are all about female psychology and that's are weird fck up place. So many variables determine the outcome so the more control you want over the outcome the more variables you need to control. If you have more specific info I can fine tune this advice even more.
REMEMBER IT'S ALWAYS AND FOREVER WILL BE about CONFIDENCE. Don't do anything you are not yet comfortable with, because some so called expert (Myself) says so, she will always know. Stick to what yu can do convincingly and remember that you are not a loser for falling to get the hook, but you are if you're afraid to try.