
So according to Margus Ots the English counterpart of "bongar" is "twitcher"
From the glossary it seems that getting around to catch a look at rarities - found and announced by others - is bonging, and collecting bird observations in general is birding.

Some highlights from the glossary
Bongarimasendus, Bonger depression: a state of mind resulting from not finding rare birds
Sender - the patron saint or good fairy of bongers, sending "raries" into the birder's way
Sponde - spontaneously found (own discovery) species; antonym: bonged species