The drop rate is low, very low. Unless you are lucky, it's normal for it to take weeks to get a drop, and nothing you can do to increase it (yet).
Being able to increase it would be nice, but right now you can expect to farm a boss for quite a while if you want all the girls.

You can't collect cash automatically either within the current limitations of the game, although there may be a change to the system when a certain big update comes (which is supposedly going to change and improve a lot of things. We don't know what the changes are, but as a lot of people mentioned it being annoying to do it manually, there may be changes to that).