The Big Poe's only appear in Hyrule Field as Adult Link while riding Epona.  Don't get them confused with regular Poes, which appear when Link is walking in Hyrule Field.  You will know a Big Poe because they fly away from Link instead of attacking him, and it will say it's a Big Poe when you put it in a bottle.  Catch them by shooting them with 2 arrows then walking up to their remains.  Make sure you have an empty bottle.  There are 10 Big Poe's to find and capture to bring to the Poe Trader, who is at the entrance to Hyrule Castle.

1) Center of Hyrule Field near a tree by the entrance to Lon Lon Ranch

2) Middle right of Hyrule Field near a gray boulder down from the Kokiri Forest entrance

3) Top right of Hyrule Field near an overhang overlooking the entrance to Kakariko Village.  Try
backing up Epona into the overhang

4) Center right of Hyrule Field along a brick wall right of Lon Lon Ranch

5) Center of Hyrule Field in front of Hyrule Castle, near a sign pointing to Lon Lon Ranch

6) Middle left of Hyrule Field on the paths leading into Gerudo Valley

7) Middle left of Hyrule Field up from Gerudo Valley

8) Top left of Hyrule Field near some bushes by a stream

9) Bottom right of Hyrule Field near a green tree and some bushes (ride through the bushes)

10) Bottom right of Hyrule Field near a rock in a grove of brown trees (only comes out when you ride past the rock from a certain angle, so is hard to get)