weight training and general body conditioning have no deleterious effects on your ability to initiate extremely fine-tuned, microscopically subtle hand movements in the art of music performance.
the urban myth of "dude, yer gonna get so huge and bulky that, uh, you won't be able to play bass.." is exactly that. many classical/jazz musicians, as well as surgeons, have embraced and extol weight training as part of their health routines.
anything done to ridiculous excess is of course not what's being discussed here. a regular routine of weights, cardio and cross training will improve your coordination, speed and stamina while likely adding years to your life. i trained hardcore for 12 years during a period i was playing remarkably well, while i was shedding a ton on my bass. got profound benefits from both.
start your program, pace yourself, expect some soreness while healing from weights days, avoid over-doing it, and you'll see great
results soon.