The Swiss authorities now have agreements certainly with neighbouring countries (France, Germany etc.) to follow up on speeding fines (and even parking tickets), as it had been too easy (worked both ways by the way, the French would rarely follow up tickets issued to foreigners). So basically if you get a ticket, it's probably wise to pay up.
If you get the full IBAN number on the payment instructions, any bank in Europe should be able to handle that for you. Indeed Switzerland is part of the SEPA payments system and when I do payments within Europe (including the UK) I don't even pay any fees and the payment arrives the same day or the day after. No idea whether a US bank can do anything with an IBAN (though it does stand for International Bank Account Number)!