Yeah should be fine for 24 hours in tank water, You can add a AA battery air pump to keep it aerated as a back up I guess.
The ph wont effect the BB, with fish I would just fill a bucket up with it treat it with prime and slowly introduce your fish to it with some of your water, I say slowly because after the move they will be stressed if you take it to fast I believe you will be stressing them an awful lot. If its discus (going from your picture) I would go extremely slow! and bring a big batch of your water for them, I find discus are the worst getting used to new water.
Not sure how your moving, but what my friend did when he moved is got some of those green rubbish bins with lids filled them with his tank water, cut a hole in the lid for air pumps and sponge filters or air stones, then tied the bins down on the ute tray and jammed the bins with pillows so they wont shake much. Didn't lose any fish but this was a 4 hour move.