Yes, you can keep this item from the task and it won't disappear from your inventory, depot, or house. I've personally tested this out. However, if you're doing the "repair" task with Bigfoot's Burden you want to make sure you put it on the floor before you report your task, otherwise, he will take it from you. I always find this item on the floor in my world in Gnomebase near where you do the mission or report the mission.
As already mentioned, you can purchase more bells from NPC for 50 gp by saying Hi -> Trade -> Items -> Yes
And if you need more details on the bell task I recommend you check out Tibia Fandom- Bigfoot's Burden Quest/Spoiler