I'm a dog groomer, so I have tried many, many shampoos on my dogs, and I am here to say that baths being 'bad' for a dog (even if 'often') are a myth; unless you're using a shampoo that was not designed for dogs in mind...such as the infamous Baby shampoo (for humans); even though gentle for humans, this is not designed for dogs, who have even more 'sensitive' skin to chemicals, than our children do...and their ph balance requirements are different.
There are shampoos that are formulated for daily use for dogs, now a days...so once a week should not be a problem, if you are using a high quality shampoo. I love Therapet shampoos; they are designed for 'frequent' use, are hypoallergenic, and tearless...and they smell fantastic.
Many of the shampoos now a days are also designed with better ph balance, and do not strip the coat of necessary oils as well, so bathing a dog once a week, or as necessary should not be a 'fear' at all...I enjoy a good clean smelling dog!!
I've also heard good reviews for Earthbath's line of shampoos, though I have not tried any for myself yet.
I have allergies, as does my hubby, to our pets...so keeping them clean, helps keep us 'sane'; I also keep my pets clean, because I have other allergies, besides to them, and they can carry different allergens in from outdoors, or find them in some of the places I can't dust, but they can hide...Lol!