If British Airways doesn't charge too much, I'm considering bringing my mountain bike back from the U.S. in two weeks for the rest of my two year stay here. What are the types of Swiss costs I might be hit with at the airport or otherwise for having something with me that I didn't purchase here? The bike is three years old. Thanks!

I'm not sure of the official legalities.
But I have brought back (and forth) mountain bikes, declared as mountain bikes, over a dozen times with out fees.

I think this would only change if you plan on selling the bike here, but I'm no expert on the topic

It sounds as though you are currently "resident" in Switzerland. In that case if you're bringing the bike in, you're actually importing it as opposed to a tourist bringing it in for a short period.
That being said, when you first came to Switzerland you presumably made an inventory of goods that you submitted to customs when you arrived. You should be able to go back to the customs office where you submitted the inventory and have the bike added, particularly if you can prove that it was already yours when you orginally came into the country.
It that's too much bother, you can try bringing it in as a tourist (could be tricky), or just declare it. You'll end up paying customs duties (based on the weight, but probably not very much) and VAT (8%) on its current value. You'll probably end up paying rather less than the airline charges you for the freight.