ACH (Automated Clearing House) is a US-based system, but I'm not sure that each & every bank participates in it. For some banks, the ACH number may be the same as the federal wiring routing number (if memory serves), but some banks will have a different number for each. Both ACH and fed-wire routing numbers are 9 digits long.
If yours is a smaller banking institution (credit union or such), it may not participate in the ACH system. If you're not getting a satisfactory answer from your branch (they should at least know whether or not they're in the system - not having heard of it entirely or being able to explain why they don't have one is a bit worrying!), go up the bank's food chain - try a different branch, the regional/national head office, etc.