Yea, don't bring cash.
There are a number of ways you can go:
1. Buy USdollar traveler checks in UK pre-trip (make sure seller is OK with that) But this will cost you and T checks are hardly used anymore and not even valid everywhere like old days.
2. Arrange with your UK bank to transfer money into a US partner bank in a city near where you intend to base out of. Confirm exchange rate is good before you do transfer and depart UK.
Then confirm money is waiting for you at USA bank.
3. Western Union (or similar) I've never done this, but can be done. FEES!
Your UK bank and US partner may nick you for some small "Fees" (theft) so find out about any and all fees (especially at USA end) before you agree. If you are in good standing with your UK bank, honestly, should be very little fees if any. YMMV of course.
You may have to open an account with the US bank. Takes 5 minutes and could be useful as you'd get a local ATM card and maybe would be an alternative to your own UK based ATM card. See if you can find a local USA address to use. This will help with banking but also with getting your title after you buy the bike. Local DMV will need an address to send you your new title and registration.
I did this other way round after I sold my bike in the UK. Had UK bank transfer to my USA bank (good friend had an account at the UK bank).
Cost nil, was done and confirmed in a few hours. Funds were waiting in my US account when I flew home.
So easy.
Thankfully USA and UK banks have some things in common regards funds transfers. Should be fairly straight forward for anything UNDER US $10,000. Over that, our IRS (govt tax agency) get notification. (no problem for UK citizen)
Hope this helps ... good shopping!