Need Advice: How do I precede?

For the sake of argument, let’s say I love this particular woman. Further, let’s say that it’s agape love, grace from God love. But there is no relationship with this particular woman other than the work relationship we share. And also, let’s say that I am pretty stupid. Now, this is the scenario I find myself. This particular woman is single and so am I. I don’t know her situation other than I know that she isn’t married. In recent weeks because of the nature of her work and mine, we have had to communicate on the processes of the work to be done. I am in a support role to her endeavors, whatever they may be. I am subordinate to her in this regard, but she is in no way my supervisor, etc. Though, I might be senior to her in age, in regards to titles, she is above me. I’m a pretty old school type of guy, and I am respectful of others, small or great. I work at a medical school. She is an MD and I am not. The people within my department I address formally as Doctor so and so, etc. To make a long story short, this woman has a very good sense of humor. Let’s just say events preceding our work relationship, has led her to address me casually but not by my name, which when I get to it is very cute and endearing to me. Let’s just say my name is John. The events preceding our work relationship had someone within the department mistakenly calling me James. Now, she addresses me as James, Joe, Jimmy, Prince James, etc. And she would sign her name other than her real name. By the way, these are all in emails between us. This has been going on a few weeks. Today, I addressed her by her formal name and in parenthesis addressed her as (Your Eminence). I signed my name as “Your Humble Servant”, and she emailed me back in response signing her name as “Lowly Subject” Like I said, I’m pretty stupid. I don’t want to jump to conclusions. I love her, and I know what love is, but I’m also realistic. I’m not afraid of rejection, because I love her unconditionally, but I’m wondering if there is something there to pursue. Is she flirting with me? It seems we are having a competition in humility, and I can’t say how much it endears me about her. To the community what should I do? What do you think? Please give me some feedback. Thanks My Name Isn't Really John