It is very easy. For instance, you want to make a 5% solution in TBS-Tween. You just put 2.5 g BSA in 50 ml of TBS-Tween, you put the sample at 4 C and after 10 minutes it is dissolved. No stirring, no mixing.
It is worthing noting that you should not let your BSA get foamy as it is generally the denatured BSA that causes/is the foam. I have found that very very gentle stirring works well. The main problem is that you have to "wet" the BSA properly before it actually dissolves in the same way you have wet genomic DNA before it dissolves properly, and very gentle stirring ( no more than one rotation of the flea per second).
In theory denatured BSA should perform well as a blocking agent in westerns or ELISAs, but I would suggest that it doesn't because the foam present will also start to nucleate denaturation of the proteins in your assay and cause increased non specific binding. Also in westerns if you let the BSA get foamy it will have very small lumps of denatured BSA that bind to the membrane and this causes non-specific binding/denaturation of the antibody and results in a very spotty filter, so dissolve it very slowly (which in many cases actually results in the solution forming more quickly than turning your stir plate to 11) and filter it to 0.22microns before use and you will have a great blocking solution!
As for the choice of solvent, I always use the buffer that it will ultimately be used in so TBST/TBS or PBST/PBS.
Souce: NovoPro 2018-02-24