Say, I am colocated in a 10mbps shared bandwidth environment? My server is taking up 1U size.

My provider says that I can only used up to 350G bandwidth?

If you're on a 10Mbps port, and 350GB of transfer is included, then your provider is allowing you to use a certain amount of data transfer on that line. The theoretical maximum of a 10Mbps line is about 3.2TB/month.

They should give you some monitoring tools to see how much bandwidth you are using so you will know how much you use during a month.

You could install MRTG on your server and monitor your bandwidth that way. Also you could ask your provider to limit your bandwith on the port to 1mbps and then you will never go over 350gb per month. The down side to that is you will not be able to burst.