What show? HD or SD? Each episode about 20-30 minutes? You can use different bit rates (if you encode it your self) to save space depending on what the content is.
I have each of the orginal 3 starwars movies backed up (running length is somthing like 2 hours and 30 minutes?) and they are 1.2gigs each at 1024bit video / 160bit audio & Original DVD resolution.
If you shrink it to the iphones 320x480 res and drop the bit rate to 768 and 128, respectively. You should have PLENTY of space.
(This is all based off H264/AAC codecs in a mp4 container.)