Just wanted to clarify, what do you mean by "VLANs showing up on the APs"? Do you mean that when you are on an individual AP's status page in Dashboard, and click into the "LAN" tab, you are seeing the multiple VLANs listed there?
If so, perhaps that's fine, I'm not sure what the intention or requirement is. Is there something that's not working at all, or not working as expected?
If the APs are connected back directly to a LAN port on the MX, you can have those configured as trunk ports and only allow the VLANs that are necessary and correspond to your wireless SSIDs and subnets, and like you mentioned just have them running in bridge mode with the appropriate VLAN tagging.
If something seems inconsistent and you have a change window to troubleshoot, try disabling and re-enabling VLANs on the MX and see if that changes the behavior of which VLANs are being seen on the LAN tab of the AP, and I'd follow up with Meraki Support with the data points you collect from there.