In general, this is not the right gesture, as bowing means acknowledging that the other party is greater or superior, and sometimes apologizing. A woman and man is expected to be good in mind, insight, and wisdom—whoever does these only bows before her/his superior.
Those who tell the truth early on may be outraged, but I'm sorry. Especially those (rather females) who seek equality, then why don't you come out and say, "men, do not bow before us, because we are not superior to you."
Of course, there are many different situations in life and anyone can do whatever they want, but this is about the general behavior. Even if you don't think so, by bowing down in front of a person, you act as if you are subject to them, and waiting for them to favor you. While this may seem like a courtesy and not a big mistake, it is unnecessary behavior.
By the way, it is wrong to expect the "marriage proposal" only from the men in general. Both genders should be able to do this. Without bending over, without giving anything away. In fact, it should be just a talk, not a "request of one side" or else you're going to "bow down on some things". Here, in general, no one intends to give anyone an unrequited favor; therefore, it is not right to propose marriage by giving something. Save your gift for no reason at a different time.
If you are constantly in the situation of asking for forgiveness from the other side, then it seems like you need to review some things. Or when you think you're making a mistake, maybe you actually aren't?
The nonsense of giving flowers or gifts without receiving them
Finally, it is weird that especially men run to their girlfriends with flowers in their hands, as long as it is unrequited. Moreover "flower" is not a woman's thing, maybe a woman wears flowery things, but she probably doesn't wear the flower you bought. Therefore, it will be as natural for a woman to buy flowers for a man as it is for a man. If man would only like "manly" things (which is generally subjective), then why is his "girlfriend" is a girl?
Celebrating gender-related days is also nonsense, but I won't go into that. Gender is in a sense a definition, not something to celebrate; however, their success, their "rise" can be celebrated, when you celebrate this as an individual by giving flowers to your lover, you are mostly making a pointless move, and even you are humiliating yourself a little. Let's give an example for those who get angry: Of course, we celebrate (in Turkey) our liberation as a country, while it seems like we are celebrating that we are "Turkish", in fact we do not celebrate that only; we celebrate rescuing it and keeping it alive.
Here, of course, I am again trying to draw a line "in general". People can do this and be good in their own way. That's why there's no point in opposing me with something like "I'll do it always", of course you can do whatever you want.