Simple dude...
"Hi, I'm Rai."
Her: "Hi I'm Rachel."
"this is Beau" (indicating the dog)
Her: "Oh he is soooo cute. What breed is he?" If she doesn't do this (or some variation) then eject. She is a heartless bitch.
Then Small talk about your dog.
Tell her you walk by here with him daily.
"Can you walk and talk?"
She will probably say she is busy doing something
"Cool, I'll be coming by tomorrow if you wanna join. Right now I gotta run him." Delayed instadate. Cost $0
The whole vibe is Hey I'm busy but I wanna get to know you, and you wanna know about me then, come walk and we will chat for 15 minutes or so....
Don't ask for her number because then if she wants to find out more about Rai the Dog Walker, she is going to have to go for a walk with him....
If you still wanna jump in her pants after the walk there is always the possibility to go to your house or hers "For a drink of water (or a coffee to warm up) If not, then set up a date, and get a number to confirm. If walking for 15 minutes getting to know each other doesn't have her attracted to you then so be it. Next.