I have an Epiphone Les Paul guitar, and I have turned it from crap into gold dust. It now plays in comparison to a £2k PRS! In some ways I actually prefer my Les Paul. The same mods will apply to your bass.
1) New pickups. I STRONGLY recommend EMG 35DC pickups, two of them. I am 99% certain you will need to route out the cavity to fit them, but lets be honest, the Epiphone bass is very cheap. get a guitar tech to fit these for you. That will get you a long way closer to that magic tone. plus, you only need to change the batterys (2 for 18v) once every 2 years with normal playing.
2) New Saddles. The string is going to vibrate from this all the time, so get some Graph Tech String Saver thunderbird saddles. They are a little rare, but not too hard to come by when you go mail order. This improves the tone no end.
3) New nut. Get a guitar tech to do this for you. Again, get a Graph Tech Trem Nut as they sound awesome! make sure your tech sets the nut to 0.4mm clearance on the E string and 0.3mm clearence on the G string. He will know what your talking about.
4) Get a pro setup. As your guitar tech is doing all of the above for you, ask him to do a Pro Setup. That is setting the string height, action, relief ect.. perfect.
5) D'addario Pro Steel strings bring out the growl in any bass, buy them and nothing else!
If you need any help, i STRONGLY recommend the book 'How to Make Your Electric Guitar Sing'. it is an incredible book and teaches you how to be a guitar tech!
I hope this helps.
