Washing all bedding and cleaning up the shelfs of the cage between full cleanings, can help keep the smell down. Also there are pet wipes for animal fur or maybe just baby wipes(?) that you can use to freshen them up between cleanings.
I don't like to spray my girls with freshener spray, but I do spray their hammocks and floor coverings. But we also use bi-oder so the smell is very min.
My rats clean themselves just fine. Certainly, there is a scent to them and their cage, but it doesn't stink, it's just part of them. It only starts to smell when the litter needs changing, so I change it. Other than that...they smell like rats, which I think is a rather pleasant smell.
But, then, I don't mind ferret smell either. I don't adore it, but it's just the smell of ferrets. Puppy breath bothers me for some reason, though...
I also have never bathed a rat. I have never bathed a cat either. Both tend to clean themselves rather well on their own.
The smell issues have never been the rat, but rather the cage. Once a week I completely wash the cage with a soapy dish sponge. Rinse thoroughly of course.
I've also found that aspen works better for making the rat smell pleasent. It doesn't smell like dirty newspaper and pee like the carefresh stuff does. And the kiln dried aspen is plenty absorbent if you change it once a week. Cheaper, and better looking IMO too.
I bathe Gregor very infrequently, because he hates it. Still, every once in awhile, he'll accumulate too much dust/dirt/lipstick on his fur, so into the bath he'll go.
I never place him near running water, because it frightens him. We use some gentle pet shampoo, and a bowl of warm water.
He is ~afraid~ of towels, so I can't help to dry him, much...just keep him warm and with me as he dries.
If you bathe, pay particular attention to the tail. Rats don't tend to groom their own tails.
If it's not too bad, I use a spray-cleaner that works rather well.
When I first got Gregor, I noticed that he smelled exactly like Graham Crackers. After the bath and the dry, smell your rat, and figure out what his smell ~really~ is. I'll bet it will be pleasant. (Some people think that Rats smell like grape juice.)