I agree with what's been said already. This is technically achievable with existing mechanics, but putting that wording below the line of every card gets very bulky and cumbersome (and imagine trying to make an Aquatic card that required other below-the-line text too). It seems fair, especially for a fan card mechanic, to call the card "Aquatic" and then be able to eliminate that text from the cards, and have the new colour as the reminder.
Speaking of colour, as with Duration, Reaction, Reserve, etc., I also believe the card should only have the new colour, rather than a mix with white. It would only use colour-blend if combined with Treasure, Victory, etc. And something like an Aquatic-Duration would probably use the "night blend" option like Night-Duration cards.
As for the mechanic itself, one could theoretically get themselves stuck (depending on the types of Aquatic cards in play) with a hand that gets played, discarded to the "bottom" of an empty deck, drawn again, and repeated. There would be an option to not play one or some of the Aquatic cards, to "reset" the pile, but then that can weaken the cards if you have to not play them occasionally. On the other hand, getting 5 Aquatic cards which all have no "+Cards", and 4 of which have +Action, +$2... this will guarantee a Province every turn. So either this design of card needs to be carefully avoided (like a Festival), or we need a slight change to the Aquatic card Type.
I would propose the following change, to defining the Aquatic card Type:
If you have at least 1 card in your draw pile, Aquatic cards are gained and discarded from play to the bottom of your deck. If your draw pile is empty, they go in your discard pile.
I think this leaves the design space for Aquatic cards a little more open. There is still the option of having 1 Aquatic card left in draw pile, gain an Aquatic card to the bottom, draw the 1 card that was there, play it, then buy a Province with coins strictly on Aquatic cards but that requires a perfect combination of Aquatic cards, likely including a village, gainer, 1 draw, and still having the right +Action and +$ .
PPE: ninja'ed!
I think your Duration comparison is perfect, and I agree. Also, I think "Aquatic" type is just fine - you don't need to change it to "Bottomdecker".