The are 8 different ways across 4 unique modes of transportation to help you travel from Hamburg to Alheim. If you're only considering the price, you should check out the train out of Hamburg towards Altmorschen, as it is the cheapest to Alheim. It's common to find tickets for as low as $44. DB operates from Hamburg to Alheim, so you book your trip with them! Take the train, even though it's more expensive, it's faster than the bus!
On your trip from Hamburg to Alheim, it is best to book as soon as possible. It won't necessarily help reduce your price by a large amount, but will ensure that you have a spot on the bus or train.
While buses have recently gotten bad coverage because of cleanliness of bus stations or winter time accidents, they are can be very convenient for travel. The best part about traveling by bus to Alheim is that it can be very cheap. That's because they usually have basic accomodations - WiFi and a restroom. Some of the Hamburg/Alheim buses' coverage has been overstated. The real thing to consider when taking a bus from Hamburg is to consider the time of travel and the density of the cities that you're traveling to. If you are traveling by bus between Hamburg and Alheim during high traffic times, you can expect to have your trip altered significantly due to traffic. Further, if you are traveling during winter, the bus schedule might be thrown off due to inclimate winter weather. Be sure to plan accordingly!
The plus side of taking the train from Hamburg to Alheim? The accomodations, scenery, and lack of Alheim traffic can usually be on point. Moreover, you can usually expect your average concessions - such as food and drinks. Most trains have WiFi these days as well. The worst part about trains are the price. While the train to Alheim is often cheaper than flying, they are generally more expensive than buses. Train prices are usually set and do not vary as much as bus prices or flights or so the likelihood of finding discounts is pretty rare.