There is never a guarantee that you will see northern lights (auarora borealis !)
Best time of the year is spring (around the equinox), second best time is in autumn (also around the equinox). Worst time is summer - not dark enough at night that far north. And of course, you won't see them if it is overcast.
The polar bears are a better bet.

I've been to Churchill twice. First time by myself but didn't pay the big bucks to ride the tundra buggy-no bear seen in the 12 hours I was there. Second time I went with my wife. We and a Japanese tourist each gave a taxi driver $20 and he took us out to where we could see a polar bear on the other side of a narrow inlet. Close enough to see but far enough that we were not in danger. Both trips were made by train from Winnipeg.
These trips were in late October/early November.
I continued my first train trip westward from Winnipeg on the Canadian which was running 16 hours late. We arrived in Jasper about 2 AM. I got a taxi out to the hostel about 3 miles out of Jasper and saw the best Northern Lights of my life on the way out there. Flying to Churchill and riding the tundra buggy is the fast but expensive way to go.
You can also take a helicopter ride out from Churchill that is even more expensive.

Jasper is much further south than Churchill but still far enoough north (for now) so that you would see many displays. I say "for now" because the magnetic north pole is migrating toward Europe, and in fact most of the spectacular displays of aurora in the past several months have been in Norway, Sweden, Iceland, Finland.

Thanks for all your help.

We are going to Churchill in early August for a polar bear and beluga whale combo trip organized by the lazybear lodge. Northern lights will be unlikely on this trip but I will report back about polar bear sightings.

We went to Lazybear Lodge in Nov 2008 on a 3 nt package. It was expensive, but worth it as it was completely organised including the flights. We were there right after Halloween, and for the first snow, which is when the bears start moving towards the shore. It's hard to pick it exactly, but the time to be there is right when the shore begins to freeze as that is what the bears are waiting for. Everyone flew in, as the train is very unreliable and long. There are other places to stay, so check it all out. Not sure about sleeping in the mobile transports, but that is available too. We saw quite a few bears and one came right up to us and hung around the viewing platform right underneath us. They book up maybe 12 months ahead, so it's something you need to plan for.