Yes there are buses that go from both train stations to the main campus.
Southampton Airport Parkway is technically quicker to get to the campus but if you're not familiar with the area you might feel a bit anxious since it's kind of not really near anything else, in case you miss the bus etc. Southampton Central probably takes a bit longer but it's more or less in the city centre so if you can't figure out the bus you need or miss it and don't want to wait longer getting a taxi will be quite easy.
Both of this assumes you're going to the main campus; if you were going to NOCS then Southampton Central is much closer. Likewise central is probably closer for UHS, although I doubt they would have an event there for offer holders...