Do you mind if I lay your bag on its side? Is it ok if I lay your bag flat?
Is it ok if I lay your bag flat?
Would you mind if I laid your bag on its side?
「カバンを横に倒してもいいですか?」= Do you mind if I lay your bag on its side? / Is it ok if I lay your bag flat? / Would you mind if I laid your bag on its side?
ボキャブラリー
~してもいいですか = Do you mind if I / Is it ok if I / Would you mind if I
カバンを倒す = lay your bag on its side / lay your bag flat
「Do you mind if I ~?」という言い方はとても丁寧なのでそれを使った方が良いとお思います。