The ring can only be destroyed by the fires of Mount Doom. Teleporters completely disassemble what it's transporting and reassemble it at the destination. Technically using a transporter kills you and makes perfect copy on the other side so it wouldn't work on the one ring.

Prime Directive

They couldn't stabilise the wormhole between the universes, leading to a catastrophic collapse, and killing the forward team in the process. Political concerns forced the project to shut down, and removed it from canon

Because they had flying dragons that you can connect to with your jombilical chord hair that's why.

Why use the transporter when there are perfectly good redshirts to utilize?

Because that would be illogical as it was Bones turn to run the tractor beam.

He found the Ring to be "Fascinating, but illogically attractive." and spent the rest of the episode wrestling with his dual nature.