This is not surprising, your right hand keeps a very different shape in the two cases. One of the most common ways of muting on the guitar when using is a pick is using your right hand palm or wrist, when playing bass with fingers the palm and wrist are farther away from the strings.edit: also should probably mention that i do play guitar, and have for years, so i dont have any problem with a pick. its only fingerpicking that im having issues with
Normally I don't suggest people should just "wait until it happens", but I very much agree that muting for a lot of players is achieved by micro adjustments of hands and fingers, directed by one's own tactile and ear perception and not much by thinking. But I do recommend some thinking or auto-analysis at least to figure out what strings are ringing out and whyThe more I think about muting strings, the less I can mute strings. My advice (as unhelpful as it may be) is "just let it come naturally." Let your ears tell your hands what sounds you don't want to hear. It may take some time, but as you become more familiar with the mechanics of manipulating your instrument, muting strings will just happen.
For instance this: "ive learned to drag my fingers across to hit the next string when playing, but all that seems to do is make the lower strings ring when i move the finger keeping it from vibrating". Makes me wonder if the OP is not just touching the lower strings to mute but actually pressing them too much, making them ring when moving away. Or whether he's using compression or distortion or even bad pickups which might emphasise small noise.