I put a bed down outside my Nether portal and hit it to set my respawn point for my inevitable death in the Nether. I received the respawn point message in chat, and proceeded into the Nether. I died, and when I respawned, I respawned under water. My portal sits on a platform above the water, but the bed was on the platform. I went into the Nether a second time and died, only to respawn in a random location in my world that is not the world spawn point.
I have uploaded some screenshots of my world showing where my portal, the bed, and where it respawns me when I die when that bed is the respawn point. I also opened a new world and to show where world spawn is. The world seed is -13935118951. The portal is at -1139 70 -1182. World spawn is 44 85 4. The location of spawn on the second death with the bed near the Nether portal set as the respawn point is 45 82 0. To replicate, enter seed. Set spawn point. Die and respawn in bed. Die again and respawn near world spawn.