When you don’t have to move (bonus card), do you pick up your separated assistant or do you have to separate another one?
Act as if you would have moved your Merchant.

So if you play this card while an Assistant is separated (from your previous turn), you pick this assistant up and play the Place’s action.

The rules say "Your Merchant stays at his current Place but you have to use an Assistant again", however, "use an Assistant" does not necessarily mean to separate one. You also use an Assistant if you visit a previously visited Place and pick this Assistant up.

References

This question gets discussed in these threads on BoardGameGeek:


Some questions about rules


André Bronswijk confirms it
Grzegorz Kobiela confirms and explains it

Bonus Card, which lets you stay where you are
Need clarification about the "Do not move your Merchant" Bonus Card


Ralph Bruhn confirms and explains it

No movement card


Ralph Bruhn confirms it indirectly