Edit: Aack! We cross posted Sleeping Beauty! Anyway:
Maybe Tolkien wanted to break the norm as it were, and have, like Child of the Seventh Age said, a middle aged,
normal person instead of some young whippersnapper bound to save the world (seriously, what is the liklihood that a young person in real life could handle such enormous quests much less being sought out by Gandalf to accompany a pack of dwarves as a burglar?). I do know that I have purposely gone out of my way to think of something abnormal when I am writing a story.
As for Bilbo and Frodo being the same age: maybe Tolkien was trying to create a bit of parallels for us to ponder, such as:
1. Bilbo and Frodo both went on a quest.
2. They both went with companions to aide them on that quest.
3. There was a high chance that neither of them would make it out alive.
So since everything was so similiar why not have their age be similiar?
A thought has come to me. They were both drastically changed when they were 50: Bilbo for the better and Frodo for the worst. A young person probably would not have been able to handle the fatigues (both emotional and physical) of both their quests (I doubt that a young person would have had the patience to wait around in Thranduil's halls). Yet, an old person would not have been able to make the strenuous physical journey. Hence, he chose a middle aged personage.
Also, when Tolkien first started to LotR, didn't he start with a young hobbit named Bingo and it didn't work? That also probably influenced his descision.
I'm sorry my thoughts are so scattered...just typed whatever came to me.