My boyfriend hit a biker with my car and I gave him my car insurance info, what's the worse that could happen?

Yesterday while my boyfriend was driving me to work in my car, we stopped at a red light and after waiting until no cars were coming from the left, he began to turn right. Unfortunately, he did not look to the right of him before turning right and a biker that was just beginning to cross the crosswalk was right in front of the car and was hit. The biker said he was fine and didn't need medical attention but his bike tires were kind of messed up. He got my boyfriends information so he could call about damages to his bike. He also took my car insurance information, on which my boyfriend is not listed as a driver. I was late for work and the driver was fine so we did not file a police report, my boyfriend just took me to work and gave the guy (and his bike) a ride home. I'm wondering if this guy ends up trying to get some money out of this (besides the bike damages which my boyfriend already agreed to pay) what he could potentially try to do?

Contact your insurance company, and report the claim. You never know if he will claim he was injured. The insurance company will complete a full liability investigation, and determine if your boyfriend was liable for his damages. At minimum, they may pay for the damage to his bike.

If you live in a No-Fault state, you may have PIP coverage which will reimburse the biker for medical expenses and lost wages(I am making the assumption this guy was on a bicycle and not a motorcycle).

The bodily injury(monetary compensation/pain & suffering) threshold requirements vary from state to state. Some are verbal, others are monetary, and still others require the injury to be "serious". If at some point he does become tort eligible, your liability coverage will provide you as the owner, and your boyfriend as the driver coverage.

If you do not report this accident, and he does file a claim in the future, your insurance company may deny coverage to you for "late notice"(varies from state to state).

he could decide that he was injured and claim a insurance claim againest you and then your rates would go up
it does not matter who was driving as long as he had a licence

your insurance will be greatly affected. the premium will be increased

Oh, GOD.... why oh WHY didn't you call the cops???
OK -- the WORST thing that can happen is the biker will head to a lawyer, then to the ER and run up $30,000 in medical bills. Then he will complain about double vision, headaches and back pain and your insurance company will exhaust your liability limits and you will be sued for the remainder -- meaning you may have to liquidate all of your assets (home, cars, dog, etc) to pay the bill. Hopefully your insurance will be enough to handle the claim and hopefully the guy isn't trying to hit the lottery with you.
Always, ALWAYS get a police report in a situation like this....