Ask about her day and her work and do whatever it takes to not let the glazed look overtake you :-).
Be polite and protective in small ways -- like walk on the outside toward the street, make sure she is safely in the car before you hop in and start it, match your pace to hers when strolling, bring her a surprise or a treat nothing outrageous but something that lets her know you are interested in her as well and that she matters to you.
I've mentioned this before but I think my favorite gift from my husband was this little hard plastic unicorn, with some fur attached lol that could clip onto things. He knew I collected unicorns and had seen it at one of the truck stops they were working on. He was almost embarrassed to give it to me because it was so cheaply made not to mention inexpensive. But, I loved it. It was one of the most touching gifts I have ever received.
You know when my husband was killed I was inundated with grief books, which did nothing but irk the heck out of me, because they all start with: "There is no right way to grieve it is different for everyone. . ." and I didn't want wishy washy, I wanted cold hard black and white facts -- you will feel this for six weeks, you will think this for 82 hours and then it will be done. . . but it doesn't work that way.
I suspect dating online or otherwise is exactly the same. We look at profiles and think oh wow he/she likes this or that, they think this or that, we should be a good match --- but then you can't even get a hello from them. I wonder sometimes if we need to reevaluate what and who we might be looking for, and perhaps we would get a hello.
While I don't think you can talk someone into relationship, I surly do think you talk someone into meeting for coffee. However, if the other person seems uncomfortable or frightened then its time to drop the persistent stance and move on to someone else.