If you're pretty sure that this friend's riding practices are what's breaking your bike every time, I think the best idea is to be honest about it. Say something along the lines of
No, you can't borrow my bike. Every time you ride it it ends up breaking, and I have to pay to have it fixed.
Your friend might get angry, but that's either because you figured out his scheme to avoid paying to fix his own bike, or he could legitimately not know that he's breaking your bike and feel like you are wrongly accusing him of something. Either way, he's in the wrong and you should not feel guilty about refusing him your bike.
Does he have a good reason why he can't just have his broken bike fixed, or why he can't buy a new one? If his bike is not too broken to ride, then why can't he just ride his own bike? Just do your best to not be rude about it, but you are perfectly justified in refusing to let him borrow your bike, at least until he can show he knows how to ride properly.
I was in a similar situation a few years ago, where a friend kept borrowing one of my good tents to go camping with his girlfriend. I didn't really mind because I was never using it at the same time, but I had an issue when he would never return it clean. He would wear his boots inside the tent, leave food wrappers in the tent, all among certain.... other messes. I asked him to stop leaving it so messy, asking that he refrain from wearing shoes and eating inside the tent (bad ideas for more reasons than my personal preference), but he didn't stop doing it. So, I told him:
Listen man, I'm fine with lending you my tent, but not if you keep bringing it back a mess like this. I'm having to spend my own time cleaning up your messes. I've asked you to make sure it stays clean several times and you never do so no, I'm not going to let you borrow it again. Get your own tent if you want to be messy.
Now, the abrupt manner of speaking I used might not suit your specific relationship with your friend, but I believe the general message should work. My friend was a bit upset with me at first, but he got his own tent and realized the work that goes into cleaning it up, and he realized I was right and apologized for it. If your friend isn't an unreasonable fellow, he will probably come around once he has to pay to fix his own bike.
