Dear
Clare,
At the age of 9, anything goes for a bike at a triathlon. Of course your equipment needs to be safe. Check out the braking distance and make sure you get a helmet that meets the standards of the snell or ANSI organizations.
Here are some ideas.
You can borrow a bike. You can find a bike at a tag sale. You can check the ads in the paper or put one in yourself. You can also have your parents check some online sites like ebay. Sometimes bike shops will have used bikes for sale.
Why not start saving your money to buy yourself a bike? Maybe your parents will 'match' the money you save.
Make sure that your bike is a good fit. Don't buy a bike that is too big for you. You need one that is just right for you now. The first bike my parents bought for me was 2 sizes too big. I couldn't learn to ride it. One day, I jumped on a little bike that belonged to a friend and off I went. Now I'm an avid bike rider.
Have fun at your triathlons.