With day game, (especially concerning women on their way somewhere) you're not going to have a lot of time to keep a conversation going.
Your "transition" needs to be your "cause", or reason for deciding to approach & stop her.
Most likely you're only going to have a minute, maybe two, if she's walking down the sidewalk, headed somewhere.
So realistically you need to be quick & decisive. "Shock & Awwwwww" kinda needs to be your Mindset. The "shock" part being: something to get her attention. followed by, something to sweep her off her feet in a sense; making her think "Awwww, that is SOOOO sweet & unexpected".
I've personally just started to understand that part.... (at least I think) but I haven't had much time to start testing different ideas yet.
But I know that you're under a REAL time constraint in instances like this.