I have a Bajaj Discover 125 cc bike for 7 years, after initial five years with Bajaj Allianz, I moved over to ICICI Lombard vehicle insurance - honestly, only because I could find an agent nearer home.
Last year I had a minor accident with my bike which damaged the petrol tank. Had taken it to a Bajaj center for repair and called the insurance help desk from there. They asked for details of the accident and said an insurance surveyor would visit in a few days.
Next day I got a confirmatory call for the claim, two days later the surveyor confirmed that the survey was done and claims would be processed. A week later my claim was settled.
I had a good experience and have continued with them since then. Recommended.