We don't need to go into the relative merits of health care in different nations to answer the OPs question.
Theft of a bike and gear will probably be covered under your renters or homeowners insurance as will Personal Liability. If you have car insurance this may also provide some coverage if have an accident while bicycling.
So before you leave check with your insurance companies about what the will cover while you're in the US.
As for health insurance the OP and his girlfriend are both covered under the Canadian system. The fact that he is a UK citizen isn't relevant because he's not resident in the UK he isn't covered under the NHS. The Canadian system might pay for some US health care costs up to the rate that's charged in Canada, but over that they won't. So its important to buy supplementary insurance to cover the excess charges and things like if you have to be flown home on a plane to a Canadian hospital. Take your Canadian health card with you and be prepared for lots of paper work if you do fall ill.
The European Union has this well sorted out. If you are a resident and travel within the EU you just take your EHIC (European Health Insurance Card) with you and this gives access to health care in whatever country you're visiting just as if you lived there. In the UK there'd be no out of pocket charge, in France you'd pay the small co-pays just like a French citizen etc.......