Ikea needs large pieces of land for it’s stores, and there aren’t many large pieces of land in New York City. So, they chose a part of Brooklyn where there are large pieces of land available.

This area of Brooklyn, called Red Hook, is very close to the expressway, but not very accessible to public transportation. Since most of Ikea’s target customers (at least in NYC) use public transportation, they decided it makes sense to provide buses to encourage customers to shop at their store. I’m sure it is worth it for Ikea. Plus, as you noted, it doubles as a mobile advertisement. NYC is probably the only place in the US where it makes economic sense to do this on such a large scale.

If they charged, I don’t think they would charge Ikea customers very much. But, it may be profitable to charge non-customers if it’s so popular. I’m not sure if there is a law that prevents them from charging, but I’m willing to bet that they would have to pay some huge surcharge like the Supper Shuttles from the airport.