Question about using a bull nose router bit in a router table
 

I am trying to make a half round edge on a piece of oak with a 1/4" round
over on top and bottom. For reasons I won't bore you with, I can't use a
1/4" round over bit on one side and then flip the workpiece over and use it
on the other side. I have a router table with a fence. I'm thinking about
buying a bull nose router bit to get the job done smoothly. Can I push the
wood along the fence with this bit or must I use a hand router and guide?

TIA.

Dick Snyder