When you recycle 2 cards from your trash, it goes to the bottom of your deck, right?

Yes, that is correct. When you recycle cards, they are moved to the bottom of the corresponding deck.

According to Rule 416.1, "Recycling cards is the action in which a player takes one or more cards from a specific zone and then puts it on the bottom of the corresponding deck."

Additionally, because you are recycling 2 cards simultaneously, Rule 416.5 specifies that they must be placed on the bottom of the Main Deck in a random order.