I don't think anyone can answer the question for how long you would be nauseous/throwing up. I've read, though, ppl sometime have it like for 1-2 weeks. As far as you don't experience electrolyte disturbance symptoms (cramps, very low BP) you only need to take care to rinse your mouth. Bile isn't usually acid, but it may be mixed with some stomach acid sometimes - rinse to protect your teeth.
At least your liver/gallbladder are detoxing. Throwing up is actually good news.