I want to make a Bedrock SMP server with my friends. Is it possible to make a Minecraft Bedrock server without using Realms services?
There is not a way to host a Bedrock server on Xbox without a player just hosting from their Xbox account (leaving the game open and always running). As you mentioned, Realms would work, but it seems like you don't want to use them.
If you have access to a PC where you could run the Bedrock Server Alpha, you could host the server there and use the DNS trick on Xbox to connect to custom servers.
You can find more information about the DNS trick here.