Should I go for the close or tease get her more interested first?

First off, I'm really not a fan of that long winded close. Much better way to say all that is "Perfect, we should split a bottle sometime soon"

In terms of what to say next, we need to figure out what the reason for her maybe is. "Stranger danger?"

If you were going to tease what would your tease be? "First I need to know you're not a hairy 300lb dude" ?

Personally I'd move to logistics, in slow and calm steps. "What's your week looking like?" You ought to be able to create all the buy-in you need (or uncover any objections) by going through logistics.

If I felt a burning need to shore it up: "Evenings on the patio are magic this time of year. What's your week looking like?"

This provides a reason to be on your patio. It doesn't need to be a great reason. It just needs to be somewhat more socially acceptable than "because you're a slut who bones strange men in under 15 minutes". Alex had a great one, "because you're bringing wine and we're not going to sit in the gutter drinking it", which doesn't quite fit here