Generally you don't buy gas bottles in Switzerland (I don't know about Suisse, though
) -- you pay a deposit and exchange, instead.
As mentioned, many petrol/gas stations (see, that's why we call 'em petrol stations) operate a gas bottle exchange service. Migrolino petrol stations are often a good bet for this.
One thing to watch out for: the gas bottle attachment on your US BBQ may not be compatible with the Swiss bottles. That's the case for many countries, including even neighbouring EU countries, but I don't know about the US. If yours is incompatible, you'll have to work out a way to convert your BBQ attachment.
Plenty of threads on EF about BBQ conversion as well as where to find BBQ gas (propane) bottles. Which raises another point -- make sure your BBQ runs on propane (which is what you get here), not natural gas. It's highly unlikely not to be propane, if you were using bottled gas in the US.