Yes you can, as long as the phone works with the Bell network. I've had several phones I've bought from other vendors and have just popped my SIM card and had service without issue. Before doing this, call Bell and ask if the phone you have is compatible, most are or may require an "unlock code" which can be found through some google searches.

Yes, it's possible as long as the phone you're transferring your SIM card to is also compatible with the Bell network. Once compatibility has been confirmed, you might have to visit a Bell store so they can activate your SIM card with your new phone. A service charge may apply.

Link: Check Phone Compatibility Here