Is it okay to get a broken blood blister wet in the shower?

Yes. A popped blood blister wet in the shower is not concerning as long as you dry it thoroughly afterwards. Blood blisters by their definition have not broken through deeper past the skin, but they can still be a source of infection. Continue to dry and apply silvadene (silver sulfadiazine) cream (can be bought otc at drug store) to help with helping. Hope that helps!
Limit water. Keeping the area dry by using a waterproof bandage or vaseline on the area for showers may help speed wound healing and reduces the risk of infection.