I have a Wells Fargo (WF) Simple Business Checking account ($500 balance to remain fee free). WF has a service called Direct Pay for business accounts. It does exactly what you are looking for.* Direct Pay costs $10 per monthly billing cycle plus a per payment fee. Payments to non-WF personal bank accounts are $.50 per payment. Payments to WF personal accounts are free. Payments made to business bank accounts are $3 each.
*There is actually a “verification deposit” of $0.00 that shows up in the account you are sending to, but no “verification steps” like trial deposits with amounts that need to be confirmed.
Depending on how often you need to do this, this is pretty cheap. I use it to mimic direct deposits for bank account opening bonuses. Since most bonuses are over $200, the $10/mo is totally worth it for peace of mind if I have to dispute with the bank that I got a direct deposit rather than just a simple ACH from one of my other bank accounts.