Bi(3+) ions are VERY prone to hydrolysis. Even at a pH equal to 0 they cannot exist, and basic salts are precipitated. In very concentrated acids, you can have clear solutions of Bi(3+), but only at low to medium concentration.
When hydrochloric acid is used, the situation is somewhat better. A complex is formed, BiCl4(-), which is somewhat less prone to hydrolysis, but also with this, a pH of 2...3 will not be feasible. You need a complexing agent in order to keep the Bi in solution at such "high" pH.
The crystals you had could be Bi2(SO4)3. At the high concentrations of acid, the sulfate may crystallize from the solution. I do not think it reacted with something in the air. It is just crystallization of a concentrated solution.