Correct use of Bonus cards in Terra Mystica
One action you can take in Terra Mystica is ending your participation for the round.

To do this, you first select a new bonus card out of the ones remaining (taking any bonus gold that exists on that bonus card).

Then you apply End-of-Turn bonuses from your existing bonus card (as you mention - there are three bonus cards that may award victory points based on how many dwellings, etc. you own).

Now the round is officially over for you, and others may now select the bonus card you just put back.

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In other words - yes; a player takes a bonus card as soon as they end their participation in the round (and some won't be available, as other players will still have theirs).