Polish influences probably, in Polish it's "do zobaczenia" (do sobachenya)
What? It's not "influence", it's just that our root бачити (to see) happens to be similar to the Polish one.
Russian didn't come first and the Ukrainian got influenced by Polish. I am not going to recite the history of Slavic languages here, but in short words - there are things like language families. English didn't borrow "see" from the German "sehen", they have a common ancestor.
It would have been "irregular" if it was spelled with two "н"s but the pronunciation was the same as with one "н". The sound is indeed different, double "н" is longer.
It is quite important for some words, for example: незлі́чений = not counted, незліче́нний = uncountable; незба́гнений = not comprehended, незбагне́нний = not comprehensible. "н" and "нн" are two different suffixes.