Concur with Eudjinn that you'd be far better off with a larger bowl. My recommendation is something on the order of 4.75" or slightly larger diameter and 2.5" depth. Having a short handle is a big plus when whipping up some lather. Squat 16-18oz latte cups, french onion soup bowls (they have handles), or even a stainless Sierra cup will do much better than that number you picked up at Target.
I had my first wet shaving experience this weekend, and wish I chose a bigger bowl! I am actually using a ramekin since it fits the soap nicely, but I do wish the sides were taller.