I believe you can drag them onto the bag to put them in it.
But a fool-proof way would be to put them in hands, Use (right -click, hold left button over bag, select hand) the bag, then put items from hand into the Bag's inventory (it acts like a container of sorts)
In some conditions the Bag lets you cheat certain scripts and keep items you'd normally lose or get extra items. Refer to Per's Guide on the site or search the forum for "bag bug" or "bag trick".