I just went through a mud bog the other day for the first time, and all the people who knew what they were doing told me to keep it in 1st gear and 4L. When they wave that flag for you to go, or however they tell you to go FLOOR it and steer straight. Don't let go on the throttle until you stop moving and they tell you to stop.
If you have the manual tranny use 4L 3rd gear and pot the clutch going into the pit and keep the foot down and dont shift. If you have the auto put it in 4L and start in first and go foot down. You could also try and shift it up as you go. I have a bronco with the 4sp that i use for mud so i dont know to much about boggin with an auto.
I also mud bog in 4L in third gear, rev it up, dump the clutch and put the pedal to the floor. I don't shift at all through the pit. Of course, if I had a big block I could probably use 4H, 2nd to 3rd. The 300 with my 3.00 gears and 35" tires don't like that too much. 3rd gear in 4L works great, though. It all depends on your gears and engine size along with tire size, because the advice to me with my setup is much different than someone with a 460 and 4.11 gears. Let us know what you have.
What I did before the first mud bog was to go find a big dirt area, put it in gear and try it. That is how I figured what I could and couldn't do.
The other thing is this. If I were to put my truck in 4L and 1st gear, it would take me a good minute to go through the pit if my engine didn't die first and I didn't get stuck. If your truck is like mine with granny 1st, you definitely don't want to do that. Way too low of a gear. Even 2nd in 4L on mine is too low. 3rd is just right in 4L, but even then I could shift if I had more power because it revs pretty high toward the end of the pit.
The old F-250 with the Thornbirds will go thru anything no questions asked (Once I for got to lock the hubs and still made it thru the pit) I think the big 390 has some thing to do with it.Anyway 4HI 2nd or 4lo third
with a f-150 breathing the juice I was always a fan of 4H second gear. You want to get the tries to spin as fast as possible. You just have to play with it. If you don't have the torque to keep them spinning in 4H do a second-third in 4L.