After having come across this sentence and "Jag bjuder!" a couple of times, the meaning of "bjuda på" finally clicked: in Dutch, my mother tongue, we seem to have this exact word, i.e. "trakteren op". It means as much as "to give someone something, or to pay someone's bill (oftentimes on drinks that have yet to be selected), without them having to expend anything". It turns out this is a pretty rare concept in other languages.
I really apologise (I feel awful because this must be annoying the amount of questions you get) but I'm still so confused with "betalar" and "jag bjuder!" could I say "jag betalar!"?
Also "He offers him dinner" and "he offers dinner to him", first one is "bjuder" and second one is "erbjuder". "Han bjuder honom på middag" and "han erbjuder honom middag". I cant wrap my head round it