Well, there is a thing called a "buffer". With bath bombs, you create a buffered solution in the tub because you are making sodium citrate. You might have an excess of either baking soda (sodium bicarbonate) or an citric acid at the end of the reaction. This keeps your water towards one end or the other of the pH scale depending on the concentration of baking soda or citric acid that you start with in the bath bomb.
There are actually 3 "equivalence points", or sort of stoping points for the reaction between citric acid and baking soda because you can have 3 sodium ions per 1 citrate molecule. What that means is you will have 3 spots where the pH will be likely to stabilize at.
Although this isn't particularly complex chemistry, it's best just directly tested! (Science is more fun if you test it than just calculate it anyway!) If I was you, I would drop my bath bombs (regular, plain formula) in different size water amounts and test the pH. Then, you can vary the temperature too and see if it has an effect. Your specific water's starting pH will have an effect though so you'll need to take that pH first.
Process I would do:
Water at room temp (~72-77 F)
Kitchen sink size
5 gallon bucket size
Bathtub size
Cold water (40-45 F)
Kitchen sink size
5 gallon bucket
Bathtub
Hot water (99-104 F)
Kitchen sink
5 gallon bucket
Bathtub
Do each location at least twice, dumping out the water with each test and testing the pH before dropping the bomb, then after it completely dissolves. You shouldn't get too big of a change between each test but it's good to check all of these.
Edited for clarity!