If you want to see the Forth Bridge, I recommend visiting South Queensferry, a charming little village just next to the south end of the bridge.
You can either go by train. There is a direct train from Edinburgh Waverly Station to Dalmeny (via ScotRail for around £5.20 one-way, traveltime 16 min). From Dalmeny it is a 15 minutes walk to South Queensferry.
The second option is going by bus. Via the Line 43 from the Lothian Country buses you can get directly to South Queensferry from Edinburgh. The trip takes around 30 minutes. A single ticket will cost you £2.80, a day-ticket £5.50 (since you will be travelling through two zones).