
No, you do not need to bathe the mourning dove. Birds will bathe themselves (either in puddles, bird baths, or even dust) when they need to.
Generally speaking, wild birds (and other wild animals) should not be taken in and cared for as pets. You are expected to have a license in order to care for wild animals -- even birds. One reason this is the case is too many people "rescue" wild animals, thinking they're helping them, when really Mother Nature does pretty well on her own.
You should read the Texas Parks & Wildlife Department's information on What to do if you find an "abandoned" animal.
Are you sure the mourning dove's mom and dad aren't in the area you picked up the dove? It's quite normal for a baby dove to fall out of its nest when its learning to fly. The parent birds watch it from a safe vantage point and make sure it gets food until it's able to fly on its own.
You can learn more about licensed
wildlife rescue & rehabilitation organizations in our Web Guide. These are the people who are legally licensed to care for wild animals; they have the training and knowledge necessary to know when an animal is truly in need of "help".