How can I soundproof my bedroom walls as cost effectively as possible?
Not sure what a fortune is and how much you are willing to do yourself.


demo drywall on walls - free
buy Quiet Batt insulation - $2 a foot or cheaper-  pack the wall cavity to the max with insulation.   If you want cheaper insulation I think rock wool is your best bet.  And I would sandwich it in.
Redrywall.  OK - Here is the big expense.  Quietrock (Lowes) works well.  It is $40-50 a sheet so that might set you back $300.  You could also double drywall - more work but less material cost.  
Mud and tape - don't know of any mud and tape that is designed for soundproofing.
There is soundproofing paint.  It helps but I am not sure how well you would notice a difference when the sounds are coming from so close.  This would be another $100.
There are soundproofing grids you can buy for your wall - some with ok designs.  These are really expensive and really out of the realm of your question.


So if you can do everything yourself you are looking at $200-600.  Another $150-200 to have someone do it for you.  Also if there are drain pipes in the walls then you will never get the full effect of the soundproofing since the 3 inches of material will probably be reduced to 1 inch or less.