My friend and I made a creative world in Minecraft Education Edition where she hosted. She wants me to play even when she is not hosting the world. Is there a way for us to share ownership?
Sadly you cannot do this as of now. The way that this is solved in other versions of Minecraft is either with a dedicated realm, or with a dedicated server, but that is not offered with Minecraft Education Edition.
Pure speculation here: you might be able to have a file stream system on both of your computers and have the game read the world on that, so when each of you plays individually that world is updated on the other person's computer. However, this might be restricted due to Minecraft Education Edition basis on Minecraft Bedrock Edition.