The word "close" is not used for bottles. You would generally hear: "Cover the shampoo when you're done using it.", or "Cover the ketchup when you're through with it.", or "Cover the mouthwash when you're done with it.", or "Cover the jelly when you're finished.", or "Cover the peanut butter when you're done."
You might hear "close" used in: "Close the box of cookies when you're done.
It must be regional, because I would never use anything other than "close" for a shampoo bottle and wouldn't use "cover" for anything other than perhaps butter in a butter dish.
A shampoo bottle is perhaps a bad example because I believe nowadays there's no cap really but a kind of pop-up spout. No person on this planet would fuss about whether this spout is left up or put down, as leaving it up won't make any difference. Same with ketchup, the bottles today may have the same type of pop-up spout, and it doesn't matter if you leave the spout up. This is why product des