A solution to your immediate problem is a company called BonVu (Bonvu.com). They specialize in exactly what you are asking for: Handling shipment of individual items overseas. They built up their business to help Europeans buy items on US Ebay. But now they provide the service almost worldwide, either direction.
It works like this: They are in Austin, TX. When you buy the bass, you have the Seller ship the bass to BonVu in Texas, which they should be willing to do. BonVu checks the packaging, does all the Customs paperwork, and books it on a plane to your country. At your end, you can pick it up at the airport, or they will have your local delivery service take it to your door. You pay BonVu for the whole deal, including any Customs or Import Fees. They will tell you the total price up front, before it ships, and you can do quick estimates right on their web site.
This service sounds expensive, but amazingly enough, it's usually less expensive overall than if you process the shipment yourself directly through one of the shippers (UPS, FedEx, DHL). They work with all the shippers, and have good rates with them.
And, most important, they know what they are doing handling all the paperwork through Customs. They do it all electronically, and it's all cleared through Customs at the other end, before your shipment leaves Austin. If there's some hangup, your bass sits in BonVu's warehouse while they clear it up. It doesn't disappear into a Customs dept forever. They ship a lot of individual musical instruments, and are completely familiar with all the rules and laws and import fees, etc. You'll get a straight answer up front from them on the total cost.
I've used BonVu's service maybe ten times to ship basses to England, Germany, Spain and Japan. Very simple and trouble-free, and not expensive.
Also, if you are selling a Bass in the US, and get an inquiry from a potential buyer in Europe, you can quickly get a quote on the full price to ship it to Europe. Let the buyer make the arrangements with BonVu and pay for it. Then you just ship the bass to Austin.