If I remove the caulk and bleach the grout is it ok to caulk over
Yes. Make sure you clean everything well, and scratch the surface of the grout if it is mouldy too.
Once you've done that, crouch in the tub and shift your weight up and down to see if the crack widens. This is to check if whatever 170 years old structure the tub is resting on is still solid. If you see it widen more than a few millimeters, perhaps you need to check under the tub for rot. If it doesn't move at, or just a hairline crack, then it's good.
I've drawn the caulk in red. If you don't make it thick enough, it'll make a dip where water accumulates (in blue) and that makes mold grow much quicker. It will last longer if you put more caulk to fill the dip so water doesn't accumulate. A tool like this helps.
I use water-based silicone, it is a lot cleaner to use than previous generation non-water based ones which tend to stick everywhere and make a mess.