I had a Betta many years ago that I buried when he passed away. I wrapped him in a tissue and gave him a proper burial in my yard.
Even when my only indoor/outdoor cat would bring me 'gifts' of dead birds/chippies/field mice, they would get a proper burial too. I would make sure my kitty was in the house so she would not see me doing this to her 'gifts'.
BTW....all of my dogs (Siberian Huskies) and kittys that have passed on over the years were cremated. I have their ashes in the containers on top of the armroir in my bedroom with their framed pics by them.
Yes...I am a total animal lover....always was.....always will be