Mail forwarding between correctional facilities is not reliable and in most cases does not happen at all. When an inmate transfers out of a facility, mail that arrives after their departure typically gets returned to sender rather than forwarded to the new location. The timing in your situation makes it particularly uncertain since the transfer happened the day after you sent the letters and postcard.
Whether your mail reaches him depends on where it was in the postal system when the transfer occurred. If it arrived at Bledsoe before he left and was already in the mailroom processing queue, there is a chance it gets held and forwarded with his property. If it arrived after he was gone, it is more likely to be returned.
The most practical solution is to resend everything to the Northwest Correctional Complex now. InmateAid will resend your letters and postcard at no charge when a transfer causes a delivery issue like this. Update your inmate's profile in your account to reflect the new facility at Northwest Correctional in Tiptonville, Tennessee, and reach out to InmateAid's support team at aid@inmateaid.com to let them know what happened. They will take care of the resend from there.
Going forward, any new orders will automatically route to the updated facility address in your account. Getting the profile corrected now ensures nothing else goes to the wrong location while your boyfriend is settling in at NWCX.