You are correct, acetylsalicylic acid is not polar enough to disolve in water. However, you can make it water soluble by treating with aqueous base, which will convert the acetylsalicilic acid to a soluble salt in an acid-base reaction (formin acetylsalicylate).
Based on experience, I know that acetylsalicylic acid is soluble in moderately polar solvens like ethyl acetate, acetone, and isopropanol.