Why was the bridge already down when the second train arrived?
It's not clear as of now why Koutetsujou (the first train) had to wait before entering the station whereas Fusoujou (the second train) didn't. 

However, a likely reason is that they were expecting Fusoujou to arrive on that day whereas Koutetsujou was to arrive on the next day, but was running ahead of its schedule.

Moreover, I don't think they expected the whole train to be filled with Kabane. They most likely only expected a few to be bitten and planned to get rid of them at the station, like they did with Koutetsujou.


  Why was the bridge already down before the train even arrived?


It wasn't. The bridge was lowered when they saw Husoujyou coming, as can be seen here: