Who are you talking to? If you are talking to a dog breeder, "bitch" is a normal word in the language of that field.
If you are talking to somebody who finds "bitch" offensive, then it would be safer to use "I have a female dog."
Thank you, perpend.I agree with the others. Somewhere between the lines, though, is the fact that we don't specify gender so much (in contrast to Latin languages), so possibly, if hard-pressed, "My dog is a she".
Otherwise "I have a dog" is fine. No need to specify the gender.