Is it safe to bottle with fruit?
Dried fruit is safer than fresh, as it is less likely to infect/introduce mold. Sterilize with vodka if you'd like. Fruit juice or puree that has been pateurized or Campden-ized is best. Look for juice with ZERO other ingredients/preservatives etc.
At what point do bottle bombs become a concern?
No idea, man. I don't bottle with a capper for my booch. I use swing-top sparkling water bottles and mason/jam jars. Both lids will pop/leak before your glass explodes.
Is fermentation just not active enough with kombucha culture to explode bottles, even with all that fructose?
I'm sure it depends on your colony makeup (bacteria vs yeast), but I get vigorous champagne carbonation from mine and I'm sure it could destroy some glass if I wanted it to.
Do you take gravity readings or anything to make sure fermentation isn't too active prior to bottling?
Kombucha doesn't take to technicalities very well because it's essentially 'wild' and the behavior and fermentation curves vary from colony to colony. Your fermentation will also depend upon how much sugar you've added and the caffeine content of your tea. In contrast to beer, kombucha is a welcome break from rigor and I prefer to treat it as a wild phenomenon as opposed to a closely controlled science experiment.
Regarding bottling: It's best to bottle right before drinking (24-72 hours) as the gas pressure is unpredictable. When I brew beer, I treat bottling like a fermentation and storage step. When I brew kombucha, bottling is just a way to flavor and consume it. I wouldn't store in airtight bottles, for safety's sake.
*all of this is from personal experience, YMMV