You must have a golden shovel to bury the money (or it won't work).
You can bury as much (or as little) as you like... but the amount you bury affects the chances of the tree growing into a money tree. If the tree is a money tree, it will produce three bags of money (instead of three fruits). If it is not a money tree, it will just look like a regular sapling (with no fruit).
If you bury 10,000 bells you have a 10% chance the tree will produce money bags when it has finished growing.
If you bury 50,000 bells you have 50% chance the tree will be a money tree
... and so on.
I have only ever had success with 50,000 or 60,000 bells before - although I am sure you can be lucky and get a money tree with less.
The money tree can be shaken like a fruit tree - BUT, the bags will not grow back. Once shaken, the tree just becomes a regular sapling again.
Each of the 3 money bags is 30,000 bells - so it is not worth burying more than 90,000 bells or you will make a loss