When you bury bells in a glowing hole, it produces a sapling which eventually grows into a full tree containing three bags of bells. After the tree has been shaken once, will it produce bags of bells again (like fruit trees)? Or does it only produce the three bags of bells one time?
They only grow bells once. I've (sadly) noticed it in game and it's confirmed in this article.
They’ll only produce Bells one time, and after you shake the money bags off the trees, they’ll go back to being a regular tree.
As a side note and as you can read in the aforementioned article, you can plant a different amount than 1000 bells. For example, 10 000b will always produce a tree which will drop three 10 000b bags, for a net 20 000b profit. Planting more (e.g. 99 000b) might produce three bags of [planted amount] OR three bags of 10 000b.
I have yet to find the percentage of chances for these events to occur, feel free to edit.