The rules on Bible covers and bindings vary enough between facilities that calling the chaplain at the specific institution is genuinely the best first step before purchasing anything.
Most correctional facilities allow religious texts, including Bibles, but their policies on acceptable bindings differ. Some facilities permit hardcover and leather-bound religious texts as an exception to the general paperback-only rule for books, specifically because of the religious nature of the item. Others restrict all incoming books to paperback regardless of content. Faux leather and bonded leather covers fall into a gray area that different facilities handle differently.
The chaplain is the right person to ask because they handle religious property requests regularly and know exactly what the facility allows. A quick call explaining that you want to send a Bible and asking whether a faux leather or bonded leather cover is acceptable will get you a definitive answer in a few minutes and save you from purchasing something that gets rejected at the mailroom.
If the facility does not allow anything beyond paperback, a quality paperback Bible is still a meaningful gift and gets through without any issues. Many publishers produce durable paperback editions specifically for correctional facility use that hold up well over time.
Once you know what the facility permits, InmateAid can help with the mailing so your address stays off the package and everything processes through the standard mail channel the facility is accustomed to receiving.