Suggestions for travel insurance with cycle cover

Specialist insurer I think would be the way to go - Yellow Jersey, as Tom mentioned, or Bikmo are just two of the options.

With the primary purpose of the trip being to take part in the LA Triathlon, you'd need to check carefully what is and isn't covered, eg Bikmo classifies triathlon as a category D activity (and won't cover personal liability - I assume only when taking part in the event itself, rather than when training in the days beforehand, but that's definitely something to clarify with the insurer).

I'd be surprised if any non-specialists would offer cover related to a competitive event - and insurers being insurers, if you omitted to mention when applying for cover that you were going there to take part in the triathlon, that would likely be an excuse for them to reject a claim even if it were unrelated to the event itself.

Worldwide cover, which you would need for a trip to the US, won't be cheap and the bike element will load the premium further (and in line with the value of the bike).

You'll obviously want the cover for eg medical expenses etc but as far as the bike is concerned it may be less hassle and cheaper to hire one out there for the duration (although of course that is no substitute for having your own bike etc set up specifically for you).

https://bikmo.com/uk/travel-insurance/activities/

Try Yellow Jersey - https://www.yellowjersey.co.uk/