Just log into both accounts and trade between them, drop trading is very risky, if something happens to you internet connection or whatever you lose out on the items.
There is a guy selling a guide on how to bypass the trade limit in the guides section. It's been verified and I just got the thing tonight and used it, worked fine for me.
But, if you don't have the trade limit just use 2 windows like ones before me have already suggested.
Doesn't logging in from the bot client and runescape client work for everyone? I can don't have to login at the same time when I use those two even in the same world.
As long as the account is either P2P or not brand new, you won't have a trade limit affecting you. Open IE and Chrome for instance, open RS on both, log in at same time and trade. Simples.