with a leg on each side of; straddling

She sat astride the horse.

on both sides of

Budapest lies astride the river.

in a dominant position within

Napoleon stands astride the early 19th century like a giant.

in a posture of striding or straddling; with legs apart or on either side of something.

adjective

astraddle , athwart , on the back of , piggyback , sitting on , straddling