I'm an old softie, so I'd say just a single rose...unless she has a favorite flower that you know of...because if you can both remember that flower and give her one, she'll be dazzled by you, you smooth bastard.
FLAMES: 21-12-3-3 TOP 10 FILMS OF 2003:  Finding Nemo,  Seabiscuit,  Matchstick Men,  Open Range,  Cold Mountain,  House of Sand & Fog,  Mystic River,  The Last Samurai,  Lost In Translation,  Return of the King
I did the low-key thing as well. Found out what she liked (in the one case,it was plants, not flowers and in one case it was daisies) and got a small of what they liked. A small spider plant, a small bunch of daisies. Because I didn't want to lay on the pressure. Married the Spider-lady.
One rose or mixed bouquet is good. For mixed bouquet, you could consider if she has allergies, although that's information you discover in later dates (i.e. don't ever ask if she's allergic to roses)
Half-dozen to dozen reds send a strong message and are difficult to improve upon for Valentine's, which is like only a month away. And the rose question will pop up again and cost five times as much :O
After I got married, I went real cheap and got some tree rose plants. It's not as nice or romantic as receiving a bouquet, but having fresh roses to cut and set on a regular basis can be fun.
My social graces consultant & I have just discussed your question. Your bio says you're 24, so we're assuming she's about that age too.
The single rose strategy is a very nice one. (Bunch of roses on the first date is a signal to run screaming. The single rose is a romantic gesture.) We both agree that the traditional colour assignments are probably moot in this context. If you've happened to notice that she likes a particular colour, go with that.
A nice arrangement is a good choice too. Definitely not big & showy, but something pretty. An arrangement is better as a pre-date gift than just the loose flowers -- with just the flowers in paper, she has to scurry off to the kitchen & find an appropriate vase, & fiddle with bla-bla-bla.
As you get to know her better, you'll get a feel for her style (& the style of her house). You'll sort out colours she likes. (Our fashion reporter should be all over that!) You'll sort out the kinds & styles of flowers she's partial to. (eg. Is she an orchid person or a rose person or a wildflower person?) Above all (as with other things) -- pay attention.
One piece of advanced listening, for next time (& the time after that, & the time after that...): When she gushes over your gift, notice any specifics in the gushing. For instance(s):
-- "How sweet of you -- that's so thoughtful." -- You've scored points for the gesture, that's good. But in this context, you haven't hit the nail on the head. Next time, try something different.
-- "These are so pretty! The pink are especially nice." You're probably good on the style; lean toward the colours that she's steering you to. (The florist can do an all-purple, or heavily-pink, or yellow & white bouquet.)
-- "Oh, I just love orchids!! And these white ones are my absolute favourites!" -- Slam dunk! Feel free to do that again. (Lather. Rinse. Repeat.)
I have one friend (just one, mind you) who's not really into flowers at all -- didn't take her boyfriend very long to figure out that stuffed animals were a better plan. Stick with the classics til you find out otherwise though.
In my opinion, daisies are the way to go for a first date. They are a cheerful looking flower (especially in the winter) and don't send an overly strong message like roses or orchids might, but they don't scream "cheap bastard!" like carnations.
Just for an FYI here is what I have heard about the whole rose color scheme/meaning thing: Red=Love/lust (something to give after you have officially been going out for awhile Pink=Like (something to give kind of early on) white=friendship (something that not dating friends may give each other, I think yellow fits here too, but I dont remember)
I too was a single rose on first date kind of guy, and I too am now single, I recommend going with nothing, but maybe spendig a little more on dinner or the entertainment for the evening.
Mr. Burns: You are of course familiar with our state usury laws? Homer:U-sur-y? Mr. Burns: Oh silly me, I must have just used a word that doesn't exist.