Well, you can meet her with a cap on but if you go further and you keep wearing it she will notice something is wrong for sure, people always do... I had a period when i started loosing my hair i was in my 20's and maybe for a year or so i always wore hats, at least when it was windy or something because i had relatively long hair. The point it, a lot noticed because it was all of a sudden and some even asked rudely, but why, but why, like humans always do... I ditched it relatively fast, cut my hair shorter and as i got older i learned to dominate my insecurities and never let them own me.
Insecurities are very easy to spot, especially by people who don't have them or by women, and they will always, and i repeat always use them against you. Don't give them the chance, bald or not, keep your head up!