Well bass fingerpicking is not much like guitar fingerpicking. On guitar the thumb plays the bottom string while the other fingers play notes within a chord shape on the high strings. On bass you generally play one note at a time, no chords or anything like that, because that isn't what bass is about. And you don't usually use your thumb, since you have better control using your fingers. Try resting your thumb on your pickup (or on acoustic, just anchor it on the soundboard) while playing the E and A strings, rest your thumb on the E string while playing the D string, and rest it on the D string while playing the G string. This will help prevent playing notes you don't want by muting them and let you reach the strings easier.