Hello,
The Bonjour/mDNS multicast is not routable between subnets. See below resources.
Disclaimer
NOTE: One or more of the links above will take you outside the Hewlett Packard Enterprise Web site, Hewlett Packard Enterprise does not control and is not responsible for information outside of the Hewlett Packard Enterprise Web site
https://en.wikipedia.org/wiki/Multicast_address
Local subnetwork
Addresses in the range of 224.0.0.0 to 224.0.0.255 are individually assigned by IANA and designated for multicasting on the local subnetwork only. For example, the Routing Information Protocol (RIPv2) uses 224.0.0.9, Open Shortest Path First (OSPF) uses 224.0.0.5 and 224.0.0.6, and Multicast DNS uses 224.0.0.251. Routers must not forward these messages outside the subnet from which they originate
https://www.iana.org/assignments/multicast-addresses/multicast-addresses.xhtml
The range of addresses between 224.0.0.0 and 224.0.0.255, inclusive,
is reserved for the use of routing protocols and other low-level
topology discovery or maintenance protocols, such as gateway discovery
and group membership reporting. Multicast routers should not forward
any multicast datagram with destination addresses in this range,
regardless of its TTL.
That means that a normal multicast router should not forward Bonjour.
Various vendors are offering the feature called Bonjour gateway (or something similar) to resolve this limitation. Maybe you can check if the ASA Firewall supports Bonjour gateway or not.