ACH is the US bank transfer network, and DGE rules name it as a permitted way to fund an internet gaming account. It is also one of the main ways money comes back: the rules allow cash-out transfers directly to your own account at a bank or other financial institution, provided the operator verifies that account with the institution. See N.J.A.C. 13:69O-1.3.
In practice you link your checking account once, often by signing in to your bank through the casino's cashier, and then deposit from it. Some casinos label this online banking, instant bank transfer or eCheck.
Withdrawals by ACH generally take longer than card deposits, because the operator processes the request first and the bank transfer follows. The account needs to be in your name: the rules bar transfers between players.
Fees and limits are set by each operator and your bank, so check the casino's banking page before you rely on a timeframe.
Source: regulations.justia.com