Hey - your very lucky (in a way) because you know the cause of your bb - imagine a bin full of food that hasn't been changed for a while - you open the lid (i.e. your mouth) and the smell that comes out ain't great.
You cure the constipation - you cure the bad breath.
First you should be going at LEAST every day (remember you have three meals a day - so going three times a day would be optimum).
There are various ways to speed this up. Firstly - if you want a quick fix there is a laxitive that is by osmosis (therefore non addictive) called movicol which you can get from the doctor (not sure if you are living in America or not - its called movicol in britain) its the main laxitive used now. That just flushes water through your system. If you clean yourself out that way you might find the bb just goes.
Long term you need to majorly up your fiber - and make sure you are drinking plenty of water (but away from meals as you don't want to dilute your stomach acid.)
If you want any more advice please message me (to my inbox here). I had a brother you suffered exactly what you have - and he cured the constipation in two weeks from eating a shit load (pardon the pun!) of fibre - and his breath is now sweet.