Looking at the compass, I note four fastners holding it in. I have been out of the industry for some time so I will give you some basics.
First the bulkhead is solid but the inner liner is secured in places only by marine putty, thus there is a void. If you thru bolt, I suggest thru the exterior bulkhead only because if you put bolts all the way thru and then tighten with lock nuts on top of the inner liner, that liner will depress inward toward the exterior wall of the bulkhead, thus not a tight seal. You may have to put spacers in between to prevent that from happening or you could put tubes from the inside of the bulkhead wall to the inside of the cabin putting the bolts thru and then use a washer and nut; thus you do not depress the inner liner.
If you use short bolts, you can accomplish the above without going thru the inner liner but make sure you have extra washers and lock nuts in the event you should drop them.
You can buy an obtrusive bulkhead liner cover but I use to get a small inexpensive plastic bowl lightly sanding it and painting it a tan color close to the color of the interior line with Krylon.
The other of course is to attach with screws on the bulkhead after hole is cut but if the screws are too long, cut them off once you have threaded them in first. Do not forget to use sealant. Hope this helps.