I do more of a powerlifter-style routine, where I focus on heavy weights at low reps. This builds strength (particularly of the tendons), with only moderate hypertrophy.
While bass isn't my primary instrument, and I am still building my plucking technique, lifting weights hasn't affected my speed or dexterity in any way. I am just as dextrous as ever on piano and guitar, and with a pick on the bass. My plucking technique is still improving, despite strength training. It takes a seriously massive amount of time, dedication, and a little vitamin H to get anywhere near the level of musclebound freakishness you see in the bodybuilding world. I can deadlift close to 500 pounds righ now, with a hook grip. That takes pretty decent grip strength. My forearms don't look much different from the average person's.
In terms of looking like Bruce Lee, your best gains will be made in your diet. You can lift weights until you are falling apart, but if you BF% is too high, you will never have visible abs, or striations. Situps won't do it, either. You need to get rid of the fat to see the muscle. As far has BL's muscular development, you could achieve it with a competent body-weight routine. Throw in some band work for additional loading, if you want. For your abs, look up Dr. Stewart McGill's ab routines. They are much safer for your spine than crunches and situps, which put a lot of uneven loading on the discs. A lot of therapists use his methods for post-injury recovery.
Regarding grippers, they do work, to some extent. They aren't going to fry your tendons, if used correctly, either. If you hammer away on them all day, you might have an issue. However, if you treat them as another workout, and use them once every few days, they can build your tendons, keeping them protected. Honestly, though, most people who aren't specifically looking to get stronger would get more than enough grip training just doing some dead-hangs after their pullup sets. If you do want to use something, you can get a similar effect by closing those springy file clips. It sounds easy, but if you try it with only your thumb, and one finger at a time, you will find it quite challenging. I promise, you won't get huge sausage-fingers, and it won't make you less graceful.
Seriously it depends on how far you are taking your Bodybuilding if you are going to cut up (get ripped) the possibility of cramping up your forearm is real other than that getting in shape using free weights and machines will not adversely affect your playing.
- I don't wanna be an Arnold but A Bruce Lee type of body would be cool. But If Bruce Lee type of body will affect my bass playing in a negative manner, then I would forget about a girlfriend if you know what I mean...!!! 
