If I bathe my dog after appliing biospot flea & tick control will it wash the treatment off?

Most likely. Why not bathe your dog beforehand with a flea shampoo and then apply the medicine?

In short yes.

Spot on treatments work by spreading themselves over the dogs body using the oils on their skin.

Remove the oil and you remove the medicine.

The dog should be bathed 2-3 days before applying the treatment to give it enough time for the oils to come back.
It is debatable that washing a dog afterwards washes away the treatment but from personal experience I find it to be true.

I'm not familiar with BioSpot, but if it is a monthly treatment just bath your dog a few days before applying each dose.

It should be waterproof, most are. Bathe your dog prior to the treatment. I believe the dog can get wet after 24 hrs of the treatment.

Buy a shampoo, like earthbath, that guarantees to not wash away flea treatment. However too much water will cause the medicine to wash off. Try not to bathe your dog too much during the month, because eventually it will wash off.

Please remember that you are applying a poison to your dogs skin. Stick to your monthly treatments. Don't re due any of them. For all you know, the treatment hasn't washed off and you'd be double dosing you dog.