first, don't use the triclhlor either- it adds CYA same as dichlor... and trichlor will also cause a pH drop.
Borax is found in the grocery aisle at Walmart...
As far as how much bleach, the amount depends on your CYA. 1.4 gal Walmart bleach should add around 3.8 ppm FC in your pool- that's the big jug of walmart 6% bleach.
your target FC is based on CYA- do you have a pool store in your area that can test your water and give you an initial CYA until you get your own CYA test?