Bonjour natively only works within a flat subnet and does not cross gateways without a proxy or multicast/broadcast bridge/route. Enabling these may cause an increased amount of broadcasts. A simpler solution to access Apple TV across different subnets is to use bluetooth.
AppleTV has a built in Bluetooth notification mechanism of its IP address, so to access an AppleTV on a different SSID and VLAN, simply enable bluetooth on your device and click on Airplay discovery. You will be able to see all AppleTVs both on your local subnet, and those in range of the bluetooth on your device (few thousand square feet). Your client can then get the IP addresses via bluetooth and can connect freely once it knows the address.
If Bluetooth is not an option, and you are using a Cisco switch
Below is the generic configuration required on the switch side, which allows a service to propagate across VLANs. Modify these commands based on the specific service needed to be accessed.
ip routing ip multicast-routing service-routing mdns-sd service-list mdns-sd PERMIT_ALL permit 10 match service-type .* service-routing mdns-sd service-policy PERMIT_ALL IN service-policy PERMIT_ALL OUT