The only way (in 2001) to get to Tarawa other than by plane from Fiji or Nauru, is by cargo vessels from Australia, The Gilberts or the Line Islands.
There are also boats to and from other islands in the Gilberts. Be there early, be prepared to wait a LONG time, and be sure you have enough drinking water. There are no facilities in the harbour area.
The bus trip from Bairiki is quite spectacular! On some places the atoll is so narrow that it is literally only a reef with a road on top. Some of the buses do a round trip in Betio, which is a cheap and effective way of seeing the town. But be aware that not all the buses going through Bairiki go all the way to Betio, ask the driver or the ticket seller.
glenn57 says in a tip that Betio is known to be rough at night, I found it to be rather rough at day, too. My son and I ended up in some kind of a shack around lunch hour, it was a mix between cafe and night club, with a couple of drunks hanging out. The food was not very good, but we did not find anything better.