So to be the safest, I’d actually do it on the source mount to avoid any potential changes on the bind-mounts.
If you have a separate partition for your /home, then add nosuid,nodev to its mount options in /etc/fstab.
If you don’t, you should be able to add an extra line like /home /home none bind,nodev,nosuid 0 0 which may do the trick (bind-mounts are weird sometimes, so you’ll want to make sure that it’s correct in /proc/mounts).