Usually, on a Fender style bass, there's plenty of room both ways on the bridge for proper intonation. This assumes, of course, that the bridge is properly installed. Most manufacturers get that right.
I'll assume you are using a good quality tuner to intonate, and using the standard methods to intonate strings at the bridge. If the other strings besides the G intonate properly, then the G string you have on the bass is probably faulty - this can happen from time to time. If you take off the G string giving you a problem and find that another one that you put on does intonate within what the bridge normally allows for, then the problem was the string. Rarely happens, but can and does on occasion. Some string companies will replace a newly purchased but flawed string if you ask.
Worn out frets and nuts can also affect the intonation to some degree as well.