I work for a large bank. Yet I do my banking at USAA.
Do NOT put your routing/account numbers online. If you do so, I would not be surprised if your account were empty in an hour. ACH can be initiated as either a credit or a debit, so a person could use the numbers to either send you money or clean you out.
As several have noted, BillPay can be used to
send money to pay your bills. As stated, if the payee is in the database, payment can be sent electronically as an ACH. If not, a paper check is mailed. Two nice benefits of this are that you don't pay the postage, and the check that is sent is NOT a check that has YOUR routing/account numbers on it. I use BillPay for ALL of my bills, regardless of whether they are in the system or not. But since you're looking to receive payments, BillPay is NOT the option you're looking for (for this instance).
For other payments, (not regular bills), for either sending or receiving, I use PayPal, and have done so for 14 years IIRC. No, they're not the best deal for their fees, but on the irregular occasions that I sell something on ebay, or make a purchase on ebay, it works for me.
Yes, there are other payment processors to look at, but I am not familiar with them, other than to restate what was already said about Sam's having an option. I think Cosco does, as well.
I hope this helps, but whatever you do, please, please, please,
do NOT put your routing/account numbers online. There are hundreds of unscrupulous Nigerians hoping that you ignore this advice.