I'm sure they floated down the river. The main source of this story is a fanc8ful book called samguk yusa. However, military events are confirmsled, I doubt 3000 virgins jumped. Maybe a few, others probably just got captured or ran away.

It happened around 661 and involved silla-tang vs. Yamato-Baekje forces. Puyeo at that time was salled Sabi and Yamato (near Osaka, Jaoan) is called Nara today.