There are no Swiss income taxes for non-resident foreign nationals, maintaining a bank account in Switzerland, except if you own a Swiss Franc account, then the 35% Swiss withholding tax applies on the interest accrued in the account and this amount is automatically debited by the custodian bank annually. Depending on your particular investment and if you are a resident of Switzerland or not, there are various other taxes such as stamp taxes, securities transfer taxes, VAT etc.
Due to the double-tax treaty between Switzerland and the US, a portion of the Swiss withholding tax can be reclaimed. To avoid this tax, you can denominate your account in a foreign currency such as EUR or USD.
You will need to provide a Form W-9 Request for Taxpayer Identification Number and Certification which is to be given to the Swiss SEC RIA as part of the custodian bank account opening process (you do not need to send it to the IRS).
Unlike a bank account, taxes may be deferred with a legal and US tax-compliant insurance company-based solution from an insurance company in an appropriate jurisdiction.
With the appropriate kind of Deferred Variable Annuity or Private Placement Life Insurance policy, the investment options for the policy's underlying investment portfolio are not restricted and when investing in foreign hedge funds for example, you are not subject to the onerous PFIC taxes as you otherwise would be. The policy's underlying investment portfolio without investment restrictions can be managed by a Swiss SEC RIA, if designated to do so (or other designated asset manager).
Professional advice on taxes, based in Switzerland
As taxes can be a complex matter you want to make sure you get it right, avoiding any unpleasant surprises in the future. You should consult an experienced tax professional, but perhaps your US tax expert is not well-versed in the tax consequences of your Swiss bank account.
There are several US tax experts based in Switzerland which have experience in the tax issues of American taxpayers living in the US and abroad.