A renters or homeowners insurance policy would cover your personal property including bikes. However a deductible would apply. For most renters policy this is not an issue as deductibles are usually $500 or less. On a homeowners policy it is not uncommon to have deductibles of $1,000 to $1,500. So for bikes in the $500-$2,000 range making a claim does not always make sense. I say this because the amount your get reimbursed is not huge and the claim will count against you and possibly increase your rate over the next 3-5 years.
One way around this is to specifically insure your bike. People often call these riders, or floaters. The upside is that there is no deductible, however it is not cheap often 8-10% of the value of your bike every year in premium. This is much more expensive than insuring jewelry or guns. The reason being is that bikes get stolen a lot.

A renters policy is cheap $15-$25 per month in addition to covering your stuff it provides personal liability. Say you or on your mountain bike at Sunderbruch flying a long having a great day. You fail to notice a family in the woods, an 8 year old walks out on the trail and you smash into her. You imagine the injuries, I can make it real scary. Lets just say a trip to the ER in an ambulance, some xrays and a broken arm, $6,000 in bills. The insurance company covers it for you!
Or lets say you find some guys riding your stolen bikes. You approach them and accuse them of theft in front of their boss and detain them till the cops show up. Turns out they weren't your bikes or they did not honestly know they were stolen. You get sued for false arrest and slander. This slander results in the person being fired from their job, there are 35 with a big mortgage and a family of 5 to support. How much do they think they will sue you for??

Anyone feel free to call me and I can answer further questions and provide you with an insurance quote. My office number is 309-762-4173.

Eric