welp they're too busy to find that item

Doha hid it there

Cuz they found the G spot

how come? if they went to that place at the same time and had sex, is there a part where doha would have time to hide that item?

Not specifically that day, he could've went before and thought it was a safe place considering bada never mentioned it. Also I find it kinda suspicious doha didn't want to go to the bed to have sex, maybe they could see the record player from there?
We basically know that doha has a link to the game and in a certain episode he killed the cousin because he went through his bag (which had multiple records) that's why I think it's most likely him who hid it.

if this is true, he's so selfish to do that. bada wanted to finish the game so badly and he's kind of destroying bada's plan just for him to have bada

True.. a real psychopath