However when I check the 'own number' listing on that phone, it still has the old, original number that it came with.

Can you make a phone call to another phone with call display? There's no need to answer the phone and incur any cost. You just want to see the number that's calling.

My Bell phone still has it's number as well.

It's not unusual for you old phone to show your old number for a day or so after it has been ported.

Do I need to do something else to have the port go through, or is it just a matter of time?

You shouldn't have to, but if the port doesn't work 24 hours after you got the confirmation text from SO then I'd call them to find out what happened.