I've also got 100s of videos in my Studio library, but I've not needed to delete many of them. There is no way that I know of to mass delete videos all at once. However, a possible work-around might be to create a "Collection" folder, move each of the videos you want to delete into that "Collection", and then delete the "Collection". It's not an idea way to do it, but in theory it would work.
Not only that, but moving a video to a collection takes more clicks (5) than just deleting it (3). Add in the 3 clicks plus typing a name to create the collection, and then 3 more clicks at the end to delete the collection, and it's significantly more work to move everything to a collection and delete the collection than to just delete each video individually.
Going forward I guess I'll start putting videos in collections when I upload them to make bulk deleting easier. (I do a short weekly overview for each class, so I build up a lot of ephemeral videos that I don't need in future semesters.) For the videos I've already uploaded, though, it looks like a long slog of click, delete, confirm.