For your cue bubbles, you'll need to select "Custom Property" > "Model Found Here" > "Component to which the annotation is attached" and then choose your PartNo property.
Normally this should show the ownership of the part and not the subassembly.
My problem is that my subassembly is considered as a part in my drawing view. I've already managed to display the properties of each of the parts on my other projects, but now I'm stuck.
However, I feel like I'm doing exactly the same thing as usual.
Unless you have a mechanically welded part, there is no reason for your sub-assembly to be a part. You could try to put the arrow of your bubble on your component (without placing the bubble right away) and then adjust the parameters as mentioned above. You'll already see if in this way you manage to find the property of your part and not that of your subassembly.