Many direct things within the text (beyond him being submissive) point to him resolutely being a bottom.
Throughout already, Asterion responds to posterior attention with flustered bashfulness and blushing giddy excitement:
-He gets visibly flustered if the MC handles his tail.
-When the MC puts his hand on Asterion's lower back, Asterion instinctively raises his tail and squirms.
-If you do the language subplot fully, Asterion writes a poem about the "warmth" he feels with the MC behind him and touching his back.
-during the kiss, if the MC grabs Asterion's rump, Asterion presses back against the MCs hand, rather than grind his crotch against the MC's.
Every indication is given that he is very deep-seatedly a (submissive) bottom.