Why do you want to go to Malmö, what's there? Is it the journey over the bridge that you want? Is the train to Malmö a separate ticket to what?

Yes going over the bridge and under the Sound by tunnel is a great trip but Malmo is not that interesting though a nice city - rather take a train from Malmo to nearby Lund, to me one of Sweden's nicest towns - a famous university town with a campus-like setting.

You could then take a train ton Helsingborg and take ferries the few minutes across the Ore Sound to Helsingor - and Hamlet's Castle you can visit then take train back to Copenhagen - the whole trip is called 'Round the Sound' and you can buy all the tickets at Copenhagen. Going to Malmo only you don't see any of Sweden really but on the Round the Sound lop you also see some Swedish countryside -- redolent to me of Minnesota or Wisconsin - old barns even look similar. For lots on trains and this loop check BETS-European Rail Experts and www.ricksteves.com.

You can take the train from Copenhagen to Helsingoer, then the 15min ferry to Helsingborg (Sweden) as an alternative but without transportation you will be limited to what you can see in the city and around Sweden. I have no idea what your passes include, they are not mentioned, but I doubt it would include a train ticket to Malmö. Another option is to rent a car for the day, you can cover alot of ground in a day plus drive over the bridge - very expensive BTW. Some sites in Copenhagen might be walkable from the centre, others will need transportation to get to.

You can take the train from Copenhagen to Helsingoer, then the 15min ferry to Helsingborg (Sweden) as an alternative but without transportation you will be limited to what you can see in the city and around Sweden>

??? The train from Helsingborg to Lund - stop over - then to Malmo and the tunnel-bridge is more than enough of Sweden I think for OP than they want - just to be in Sweden basically.

We took the 99 bus from Central Square to Malmo. Very easy. Not a lot there but it was right after Christmas and it was fun to stroll around, enjoy the lights, and get cute Scandinavian Christmas ornaments on sale.

You can get a transportation pass which covers Copenhagen and surrounding area--Roskilde is just out of bounds. Little help at the airport, but the main train station had an attendant to help navigate the automated ticket machine for what we wanted to do--it actually did not work but the train conductor on the way to Roskilde accepted our explanation and did not require an extra payment. I believe that I discussed the pass in my trip report; click on my name to find it.

Copehagen Card may cover sort trains in Denmark like to Helsingoer, Denmark perhaps not sure. But not Swedish trains.

Airport, the heart is a big place. I'd look on google maps for the nearest bus or train stop and work out which is the better option. The buses are normally bang on time and in our case over stopped just outside our hotel, while the station was a hefty walk away.