I'm a language neuroscientist so I love to run little experiments. I also love how language shapes who we are and how we think.

Compare the following three simple date planning sentences.

  • How about we grab a drink?
  • Let's grab a drink!
  • Would you like to grab a drink?

The 1st person plural imperative ("let's do this") shows leadership and inspires camaraderie. It shows that you want to spend time together, but also implies that your having fun is not entirely contingent on her response (outcome independence). There's also no demand for evaluation of the idea: "Would I really like to grab a drink with this guy?" She can still decline but that's not embedded into the statement like it is into the questions.

"How about we grab a drink?" is okay. It still shows that you want to be with her together and the phrasing is pretty positive and relaxed. The yes response is still implicated in the question albeit not as strongly as the imperative form.

"Would you like to grab a drink?" is pretty damn weak. It puts her in the driver seat and it's too vague with regards to intent. Maybe she does want a drink, but there's nothing in it that relates to you and her drinking together. It forces her to evaluate you immediately and that may not always work to your advantage.

tl;dr: Let's grab a drink!