I started posting this as a comment and it became to long. Joe's answer is awesome, for the record. You should read it in conjunction with this one.
At 7 years old, color is important. You need to be prepared for the fact that no "parent logic" is gonna override the "but I want pink, Lizzy has pink and I want pink too". That said, this is an important opportunity for a lesson, or several lessons.
First, IMO, you can teach cost v.s. quality v.s. lifespan. For example, I took a look at my local bike shop and there were basically 2 options. $700 for a bike the right size for a seven year old girl. This bike would work for a couple of years and have to be replaced because of size. Or around $1,600. The more expensive bike would last them into their late teens. It's adjustable enough to keep with their growth long enough that the next bike they will buy should be as an adult (or close to it). Neither of these options come in pink however. Of course you can always go to Target or the like and shop around $200, but those bikes may or may not make it a year. They may have them in pink. Now this is a trick lesson to try to impart. Specially if it's their first bike, or they are not using their own money. You can try to point out all the benefits of the more expensive "last forever" bike, but it's going to be boring, and not really compete with pink. Rather you can impart this lesson or not is going to depend on the child, and why they want a bike. If your thinking family biking runs, and doing it as a hobby, then push for the more expensive bike. If they want a bike because everyone else has one, and she's not really an outdoor person, or your not an outdoor family, then you can use the expensive bike as a "too much for the goals, more isn't always better" lesson.
Next, you can teach "future proofing" purchases. IMO this is an important lesson to teach when ever you can. At 7 not much is gonna last more then a few months. A bike is going to last a long time. So you can use it to teach "What you like today, you may not like tomorrow" and the value of making choices that you can change later. Use examples like kids cartoons that they out grew. Or stuffed toys that they don't find "cool" any more. This works especially well with things they liked, but don't like cause "it's for babies". Show them that a neutral color with pink trimmings, baskets, tassels, handle bars, tires, whatever means they if they decide they don't like pink they can change it later for much less then the cost of a new bike.
Third, teach proper bike safety. There is a lot to owning a bike, and a lot of this is going to depend on circumstance and goals. But bike safety is important. The proper way to ride in the road, or on a shared path. Rather to be on the sidewalks or bike lane. What side of the road to ride on. Rather or not to ride on the sidewalk. What are good areas and bad areas to ride in. Again this is very dependent on where you are. I live in a city, and there is a decent amount of support for biking. That said, there's no way I would encourage my 7 year old to ride in the bike lane. I would teach them to ride at one of the bike trails, to walk the bike when crossing the street, not to ride on the sidewalk, and how to ride in the streets around the house. I would also set some boundaries about where they could ride alone. But in among all theses are discussions about laws, lights, reflectors, clothing colors, helmets, and the like. Perhaps even how pink can't be a color for some of those.
In short, a bike is a big purchase. Color is going to be important, but you should, IMO, use this purchase as a lesson on how color should not be "the most important" thing, and start discussions about how boring things are important too. At 7 there are not a lot of opportunities for this, might as well use them when you can. In the end be prepared, either way, for the 7 year old to act as a 7 year old. You may have to move your foot in a downward direction, or accept that pink is what she wants and work around it. In either case, make sure you add your needs (like safety and reliability, re-uasability, and cost) over the top while still remembering it's her bike, and she's the one that has to ride it.