I've tried a few things that do not cause plants to respawn:
- Saving and loading
- Fast travel between two locations (ie, changing zones)
There's a timer for it, to be sure. I picked a Black Cohosh plant near the first town, and checked on it periodically as I ran other quests in the game. I estimate it took between 3 and 4 hours of "real" time for the plant to regrow.
After I purchased and upgraded Gossamer End in Canneroc, I did some experiments by picking the plants in the basement and then sleeping for extended periods. There are three types of plants that spawn in the basement of the home:
- Star Thistle, which respawns after approximately one day in game
- Scarwood Tree, which respawns after approximately two days in game
- Black Cohosh, which respawns after approximately three days in game
I'd say from this, you can't really expect to "farm" wild plants in an area without some manner of advancing the game time. Any bed will do, but with the amount of time involved, you're probably better relying on new areas and the stocks of merchants to accumulate ingredients.