I want players in my Minecraft world (Bedrock Edition) to be able to use the function command without being given operator permissions. Is this possible through the use of behaviour packs or commands? Is it possible at all?
So you probably need to do custom triggers, like dropping a specific item, jumping five times, etc.
You could run a function when a player drops a specific item, with a repeating and always active command block. The command would be
execute @e[type=item,name=<name of item in quotes>] ~~~ function <name of function>
<name of item in quotes>with the name of the item you want to detect the drop of in quotes.
<name of function>with the name of the function that you want to run.