The City Pass only covers zone 1 to 4 which is equal to Copenhagen and Frederiksberg Municipality and the island of Amager where the airport is located. It does not cover the 30- and 40-zones and thus it doesn’t cover Ballerup. The most economical way of travelling from Ballerup to Copenhagen (and beyond) is to use 10 trip clip cards. These cards are almost half price compared to individual tickets. With clip cards (and also with individual tickets) you pay for the number of zones that you trip requires, and you can travel within the entire greater Copenhagen area which extends to Elsinore, Hillerød, Roskilde, Køge and a bit beyond. The cards are available as 2, 3, 4, 5, 6, 7, 8 and 9 (all) zone cards with 10 stampings on each card. You pay for your trip by punching your card(s) the required number of times at the beginning of your journey. The cards and the stampings can be combined and shared in any possible way to form a trip of the required number of zones. E.g. a 5 zone trip can be made by stamping a 5 zone card once or by stamping a 2 zone card once and a 3 zone card once, a 6 zone trip can be made by one stamping on a 6 zone card, 2 stampings on a 3 zone card, or 3 stampings on a 2 zone card. The amount of zones that you have to pay for is not the amount of zones that your trip leads you through, it’s the distance measured in “zone widths” from your origin to the zone furthest away from your origin on your trip. On each bus stop and train station, there is a small map, where you can see how far you can travel for all different amount of zones paid for, so you don’t have to find out yourself. When your card(s) are stamped at the beginning of your trip, you can travel freely between the zones paid for within a set time frame, you can use any mode of public transportation you want (bus, S-train, train, metro, harbor bus) and you can make an unlimited number of transfers between all transportation modes as long as you are within the validity of your ticket. You can even travel back again on the same stampings if you have time. Your ticket is valid for 1 hour if you have paid for up to 3 zones, 1½ hour up to 6 zones and 2 hours for trips over 6 zones. From the airport to Copenhagen, it’s 3 zones, from Ballerup to Copenhagen, it’s 4 zones, and from the airport to Ballerup, it’s 5 zones. You could buy a 4 zone card for your travel between Ballerup and Copenhagen, but it is more flexible to buy a 2 zone card and a 3 zone card, since you with these two cards combined can form a trip of any number of zones. There is one rule, though: there is no one zone trip. For all trips, even when completely within one zone, you have to pay for at least two zones. 10 trip cards can be bought at all staffed train stations. If you are staying near Malmparken station, in Ballerup where many businesses are located, note that this station is unstaffed.
If you make a lot of travelling within one day and you travel far, a 24 hour pass covering the entire greater Copenhagen area (not the City Pass) is more economical than 10 trip card, but otherwise, 10 trip cards are best and most flexible. Note however, that unused clips on 10 trip cards cannot be refunded, so factor this in.