In my opinion, you're looking for a reagent which will react with aluminium oxide to form a new (ideally water) soluble compound, but will leave the other components untouched. This would allow you to filter out of insoluble Carbon and Bismuth which could be returned to the beaker. The filtrate would contain your new aluminium compound which could (if you wanted) undergo further reaction to produce aluminium oxide, your original compound.
As a possible clue, you might like to think a little about the reactions of aluminium oxide and common bench acids remembering of course that you do have to consider the reactions of these with the Bismuth present also.
P.s. Where are you from? Just curious as I noticed that you spell Aluminium the correct way, so clearly not the US!