Your bank account is linked to coinbase, right? You're not holding bitcoin elsewhere in an "offshore" account, right, so you're not using an actual wire transfer? If you're just dealing with Coinbase then your bank will see where the funds came from and you should check with your bank what their policy is on bitcoin. My bank was opposed to bitcoin and accepted the coinbase transfer one time only and I was warned not to do it again.
Good advice. I will make sure before I do the transfer that it is ok. I have a couple of bank accounts with different banks, so I can find one that will work before I transfer the funds. All my accounts are in the USA, so nothing is offshore.