I’m 34 so I reserve the right to change my answer in 3 months when I’m more qualified. I’ve also been happily married for 14 years so I’m largely just guessing at what I would be looking for.
Lack of drama is a big thing. By now we’re sick of dealing with all the childish BS which is why guys usually finally give up dating 20 year olds by 35. Somebody who is mature and knows that it’s too late to change them. Somebody who is not incessantly clingy but doesn’t swing all the way to being impartial.
As for actually asking out, approachability is obviously the key. This is my opinion and may be invalid, but I believe the best guys are the ones that are uncomfortable about asking you out to begin with. It’s like a job applicant that’s really bad in an interview. Might just be because he holds down a job for 10 years at a stretch. The guy who’s really good might have gotten that way by losing a lot of jobs.
The most important thing guys are looking at (those that aren’t just looking at your chest, that is) is “is this somebody that I can enjoy life with?” Somebody who is jovial, upbeat, active, passionate and optimistic trumps somebody who is sexy and depressing. How happy do you make me when I talk to you? How often do you make me smile?
I’d like to think that by 35 most guys have that figured out. I’m probably wrong. Short skirts and cleavage is probably the scientifically verified answer, but I’ll keep being optimistic.