In version 1.3.0 and higher, all bags will drop from different types of entities (mobs) based on their rarity. Each group has a loot table, which you can override to customize drop rates.

Entity group loot tables are found here: 1.16.x

For more control, there is a loot function which will set the bag type (as all bags are a single item). You must use this function to get the correct bag type. The function name is treasurebags:set_bag_type and it has one property, type, which is the bag type ID. See the example below.

This particular file (which is the bat loot table) has a single pool with one entry, which has a 10% drop rate with a 2.5% bonus per looting level, as well as requiring a player kill. You can of course omit these conditions if you like. You would probably want a much lower drop rate for most bags as well, maybe 1~5%.

Note that if you have more than one treasure bag entry in a pool, you need to include the entryName property with a unique value for each entry. This is needed anytime you have multiple entries of the same item.

For the bag type, this should look like your_namespace:bag_type. In this example, the bag type file is located at data/chaos_loot/treasurebags/bag_types/bat.json, which translates to a bag type ID of chaos_loot:bat.

Converting JSON file name to bag type ID:
data/namespace/treasurebags/bag_types/file.json => namespace:file

{
    "pools": [
        {
            "name": "treasure_bags",
            "rolls": 1,
            "entries": [
                {
                    "entryName": "bat_bag",
                    "type": "item",
                    "name": "treasurebags:treasure_bag",
                    "weight": 1,
                    "functions": [
                        {
                            "function": "treasurebags:set_bag_type",
                            "type": "chaos_loot:bat"
                        }
                    ]
                }
            ],
            "conditions": [
                {
                    "condition": "killed_by_player"
                },
                {
                    "condition": "random_chance_with_looting",
                    "chance": 0.1,
                    "looting_multiplier": 0.025
                }
            ]
        }
    ]
}