The main CITES thread is the best source of information on this.
My short version?
Buying and selling instruments that contain shell inlays, or any type of rosewood (and the variants that have been added to CITES, like Bubinga) across national borders is a colossal pain at the moment.
Travel for individual musicians is much simpler, as there is an exception for personal travel and performance. In theory, a CITES passport for your axe is unnecessary.
I keep a eye out for this, and so far I haven't heard of any electric bassists running into trouble while touring. Personally, I would still carry dated photos and receipts to prove that I already owned the instrument before I left, and didn't buy it while I was out of the country.
However, Customs agencies are still struggling to deal with this, and the situation is constantly evolving.
The best way to avoid any issues, is to avoid fancy inlays and rain forest woods. Pretty much any standard maple-necked solidbody Fender bass or offshore copy should be safe. So is my maple-necked Dingwall.