OP. The problem you will have now is there will be hundreds of baby ticks and u hatched tick eggs in your house. They will keep going back onto the dog.
You need to buy a product that will kill these ticks before they get to your dog. Your home has to be retreated several times over a few weeks because the products don't kl the tick eggs, which otherwise will hatch and start the problem over again.
Your dog does not need a tick bath. Use a spot on liquid once a month, applied to the back of the dogs neck. This kills any ticks that try to feed on the dog.
These spot on are cheap too if you get the brands that are not imported.
Keep a close eye on your dog as its had so many ticks there could be a chance it will get a disease off them.
If the dog goes off its food or acts lethergoc, get it to a vet ASAP as they can die from disease transmitted by the ticks.
Good luck. Your vet will be able to advise you about the house and dog tick prevention products and how to use them.
If you simple give the dog a tick bath, they ticks will come back time and time again as they are on / in your property now.