If it is the other strings resulting in the noise, try working on muting with your fretting hand.
Otherwise it I could be dynamics which I found a lot harder on electric than acoustic.
Try setting your amp to mid gain (just not near full gain) where if you strike the strings hard you can hear it break up, but if you pick softer/normally it cleans up. The mid gain gives you done head room to pick normally without extra noise and when you want it to grunt at you, you just “dig in” a bit harder. Experimenting should work best on clean with your bridge pickup.
Hope I’m remotely on the right track…