How to override a vanilla feature?

Create a datapack in which you change the vanilla rose bush loot table to any item you like, then merge that datapack with your mod. That loot should go in - your mod\data\minecraft\loot_tables\blocks (rose_bush.json goes here)

This is the rose_bush loot table:

{
  "type": "minecraft:block",
  "pools": [
    {
      "rolls": 1,
      "entries": [
        {
          "type": "minecraft:item",
          "conditions": [
            {
              "condition": "minecraft:block_state_property",
              "block": "minecraft:rose_bush",
              "properties": {
                "half": "lower"
              }
            }
          ],
          "name": "minecraft:rose_bush"
        }
      ],
      "conditions": [
        {
          "condition": "minecraft:survives_explosion"
        }
      ]
    }
  ]
}

reference: https://www.youtube.com/results?search_query=custom+loot+table+minecraft

You don't even need to do write one manually then merge. Just create a loottable in your workspace, set it to a block with the name rose_bush, and there you go.

Ah I see what you mean now.  I believe if you edit the blockstates/loot tables in vanilla MC, you should be able to change it to not drop anything. I'll look into the data files later since I'm curious myself and will update ya.