It's a Lottery. Best chances probably at Bangkok Bank or Kasikorn. Bring your Passport, a certificate of residence and if possible, a recommendation of your employer/ company, as you're on non-b.
It's never the Bank, who forces you to buy an insurance. It's the staff who want's to make some xtra money. Most banks are trying like that now. If it's only about 2000,- THB, just accept instead of paying some agent. Agents often ask for 5k for opening an account.
I know mini van rides only from visa runs, a couple of years ago. I never felt well. Today I avoid them whenever possible. Every week you see news reporting about horrific accidents, mostly caused by speeding or sleeping drivers.