Question: "Does the Bible say anything about teleportation?"
Answer: Teleportation is the act of instantly moving from one location to another without physically traveling the distance in between. It is definitely theoretical, although there have been some recent scientific advances in teleporting energy (not matter). But, for now, teleportation is science fiction. The transporter in Star Trek and the mutant Nightcrawler in the X-Men comics and movies are some of the more popular examples of teleportation in science fiction.
The Bible does not mention teleportation, per se, but it does give at least two examples of miraculous transportation. In John chapter 6:16–21, when Jesus got into the boat after He walked on the water, “immediately the boat reached the shore where they were heading” (verse 21). This is not necessarily an example of teleportation. The word translated “immediately” does not have to mean “instantly.” It could just mean “very quickly.” Whatever the case, after Jesus got into the boat, it either was teleported to the shore or was in some other way brought to shore very rapidly. Either way, this amazing miracle is often overlooked.
In Acts 8:26–40, Philip led an Ethiopian eunuch to faith in Christ. After the eunuch was baptized, “the Spirit of the Lord suddenly took Philip away, and the eunuch did not see him again, but went on his way rejoicing. Philip, however, appeared at Azotus” (verses 39–40). Again, while this not necessarily an example of teleportation, it is definitely an instance of miraculous transportation. The Spirit miraculously transported Philip from a wilderness between Jerusalem and Gaza (verse 26) to a city about thirty miles away (verse 40). Whether this miraculous transportation occurred instantly or took some time, the passage does not say.
God is omnipotent and omnipresent. Teleportation would, therefore, definitely be within His ability. Whether the two examples above are genuine biblical occurrences of teleportation is unclear. What they do demonstrate is that God is able to supersede the laws of travel and significantly expedite the process. If God desired to teleport someone or something, He could do so. Whether humans will ever be able to invent a device to teleport someone or something remains to be seen.