Does my cat have fleas?

I have a indoor cat who has recently went outside in my backyard about two times. I noticed black/brown speck on her head. I moved her fur and i saw a flea but it moved and went somewhere else in her fur where i couldn't find it. Now, i see brown and black specks on her body especially her head. Are these flea eggs? Also, are there any ways to get rid of fleas? i Know i can give her a bath with flea repellent shampoo (which i have) but are there any other ways to get rid of the nasty fleas because my kitty hates water and baths? Please be as specific as possible. Thank You!! :)