I've been learning this bass solo by Jean Baudin. And he has an 11 string bass. I have a 4 string. Only at a few parts in the song, he plays notes higher than my highest F on the G string. So my question is: How high can I tune my G string without it snapping?
Be very, very careful. You're worrying about the string snapping. You should also be worrying about damaging the neck of your instrument.
A bass string will go very tight without snapping. If it does snap, you risk injury. I've had a nasty cut just from a guitar string! If the instrument breaks, you also risk injury -- and you've broken your instrument.
Instruments are designed to carry a certain tension. Exceeding that tension can damage them badly. Keeping them below that tension for long periods is also not a great idea.
The right way to get a higher pitch is to use a narrower gauge string.
String manufacturers produce charts telling you what tension strings exert at various pitches. Here is a link to D'Addario's.