For what I have read, regurgitation is a common weaning or juvenile behavior and it has nothing to do with gender but with age or maybe I should say coming of age? I would guess that, depending on the angle one looks at it, it could be said that regurgitation in birds that are not sexually mature IS about bonding - maybe as in acceptance into a family group? You know, the way a semi-grown or very young dog licks the inside of the lips of an older dog as a way of 'getting accepted' into the pack?
As to adult birds regurgitating, well, it's one thing in the wild and another altogether different in captivity - but that also has to do with the actual conditions of such captivity. I have had homosexual couples, both two males as well as two females (have one right now, as a matter of fact) but although they had every other behavior of the mate-bonded, preening, sticking together, sharing food and even having sex with each other, nesting and even laying eggs in the case of the two female pairs, I never saw them feeding each other - neither the males nor the females pairs. I think I should point out that all three of these homosexual couples were of the same species (tiels, cockatoos and amazons) with the exception of the amazons which belonged to different ones but, in all honesty, amazons bond with any other amazon species so easily and they are SOOOOO similar in looks and behaviors that I don't think they even see each other as different.
Now, in the wild, male birds regurgitate for the female as part of their courtship BUT, for what I can tell from what I have read, this doesn't happen at the beginning of the courtship but after the female accepts the male when they first 'hook up' and, in the following breeding seasons, when they are already looking for a nest or even building it. I have no experience breeding parrots but I do have extensive experience breeding canaries and observing parrot pairs go through the motions of breeding although only one of these pairs was a male and female of a large species (again, amazons) -the others were all lovebirds, budgies and cockatiels and although two of the homosexual pairs were of a larger species, I am not using them as an example. What I have consistently seen in all species is the male feeding the female as part of the courtship as well as later when she is sitting on the eggs and, later on, the babies.
In captivity, behaviors are not 'normal'. In the wild, a bird is only imprinted to its own species, precisely tuned to the seasons by light and diet, and has a large pool from which to choose a mate while, in captivity, most pet birds are kept producing sexual hormones too long and even all the time, they usually do not have a single other bird of the same species and opposite gender to choose as a mate AND they are further confused by their imprinting to humans so they, sometimes, end up presenting breeding behaviors that are not species, gender or even season appropriate. Personally, I've never had a single bird regurgitate to me. During breeding season they do get super 'mushy' (as Seagoatdeb said

), jealous of other birds, defensive of their cages, very chewy and, if given a nest, they gladly work on it and even spend long times inside of it but they never get to the point of regurgitating to me, to a toy or to any other bird.... the male Senegal has been dancing to the female, wooing her with human as well as parrot words and 'working' on a nest tirelessly but she hasn't accepted him so he doesn't regurgitate to her.
As to how does a bird tell if the other one is a male or a female? Well, for one thing, birds recognize the differences only in their own species because it's done through sexual imprinting in the nest and it's thought to be done through sounds (the 'voices' of the parents and the fact that in songbirds, only the male sings) and plumage (with the only birds that know instinctually been brood parasites like the cuckoos, for example). Brighter colors, different plumage or other physical characteristics (like a longer tail or crest, for example) are all markers of gender. One thing we need to take into consideration is that we neither see in UV nor are we birds so even when a male bird of a sexually monomorphic species looks exactly the same as a female bird to us, it doesn't mean they all look alike to each other and cannot tell, it only means WE cannot tell. Filial and sexual imprinting are both survival traits which ensure the preservation of the species - if a bird knew a bird of another species to be of the opposite gender and 'felt' it was OK to breed with it, there would not be the large degree of avian speciation we have. Again, it's different in captivity where imprinting was screwed up by hand-feeding and there is no choice for them but to mate with whoever or whatever is handy.