How much such self funded searchers have set aside (on average)?

We’ve bucketed it into four camps - 1) living expenses (YMMV) 2) search expenses 3) diligence/legal expenses and 4) equity to invest in the business.

You need to be prepared for the search to take up to a year, so you'd want to have that much in living expenses ready, if you won't be working outside of your search. Obviously the more you have set aside the more time you give yourself, but you should always have a minimum of 6 months living expenses set aside regardless. You also want to identify the amount you'll need to bring to the table in down payment and closing costs for the business you eventually purchase and have that readily available, too.