What will be the final volume of your working solution?
You must use 1:10 dilution of the BSA stock solution to give you 10%.
For instance, if you want to prepare 1mg/ml BSA stock, then you weigh 10mg BSA powder in 10ml milli Q/distilled water. While dissolving BSA, gently swirl the tube till the BSA dissolves completely.
From the stock, if you need 10% say in 10ml, then you use the formula
C1V1=C2V2
C1=100% BSA stock (1mg/ml)
V1= volume required
C2= 10% BSA solution
V2= 10ml
Therefore, 100 x V1= 10 x 10
V1 = 1ml
So, you will take 1ml of 1mg/ml BSA stock and make up the volume to 10ml with milliQ/distilled water to give you 10% diluted BSA solution (0.1mg/ml).
For a 10% BSA-solution, dissolve 10 g in, say, 50 mL of solvent, and then make the solution to 100 mL in a volumetric flask. Dissolving BSA is difficult, as it becomes gluey upon addition of water, you need to vigorously stir for a couple of hours or o/n (but avoid foam!).
The solvent you use depends on what you want to do with the solution later. If your experiment requires PBS, then use that for dissolving. I generally avoid dissolving proteins in pure water, a 10 mM HEPES or Tris buffer is a good alternative if you need the solution for several purposes.