There are plans to extend the Train line from Tehran to Bam
The city stretches out a lot so you might want to use a savari to get to the arg.
The ancient citadel of Arg-é Bam probably has a history dating back around 2000 years, to the Parthian dynasty (248 BC-224 AD), but most buildings were built during the Safavid dynasty. The city was largely abandoned due to an Afghan invasion in 1722, which ended Safavid rule.
The main attraction, the ancient citadel of Arg-é Bam, suffered badly in an earthquake in December 2003. Today little is still to be seen and access is extremely restricted; there is only one main access path still open to the public and the castle on top of the hill is out of bounds.
Akbar Guest House is probably still the cheapest place in town, but it is still unfinished and being rebuilt. Be very careful to avoid being grossly overcharged: in November 2012 I was charged 250,000 rials (he originally wanted 300,000 but gave me a 'discount') as a single person in a room with a shared bathroom that had no hot water and no breakfast. This is about twice as much as the room should cost, and by far the worst value accommodation in my month in Iran. I would recommend staying in Kerman and visiting Bam as a day-trip, as the Arg can be seen in an hour or so. Only stay in Bam if you are traveling overland to Pakistan and have an absolute need to stay here.