It could be a cool thing to do, just to have done it.
I assume you are not actually wanting to dive with it, but just being able to go a few feet below the surface?
If you want to build a diving helmet that is actually functioning i would recommend that you build it from scratch with this in mind rather than changing an existing helmet. I would actually rather look into getting a real diving full face mask or helmet and pimp that out mandalorian style...
However if you just want to go below surface for a few minutes you should be fine.
I assume that you are going to do tests on depths where you can simply stand up if something breaks and not where you can not reach the bottom.
As you say, a continuous flow should do the trick if you att a outlet valve near the top of the helmet.
In that case you wouldn't have to worry about a release valve to when you surface either.
The higher the flow the more CO2 is released, so keep the gas flowing!
Hight flow also shortens the length underwater, If you have a 5 litre bottle you should still get a few minutes from it though.
When it comes to wether a strap will be enough to keep the bucket on, it is all a matter of what kind of strap, the volume of the (sealed) bucket and the weight of the bucket. Archimedes law, you know...
Depending on what you propose to do you can get away with much.
If you consider a free flow design and keep the helmet upright you can probably get away with it as a sort of primitive diving bell for you head. and not need much else that an airtight dome and open bottom...
But with all this being said, as a former diver, i would not recommend anyone risking their life doing this. It is dangerous if you do not know what you are doing.
