This is a truly difficult question. There are online calcs that help with this. Here is one.. The problem is your not really trying to serve liquid with 5.1 volumes at regular pour. If that was the case you would need tons of tubing.
3/16 tubing has the most resistance to prevent foaming. I believe it's 2-3 psi/ft. If your beer is carbed to 5.1 volumes (45psi at 45°) I think I would start with 20-25 ft.
Once again, chill the bottles, line, and filler. In fact, place them in the freezer the night before filling.
Also, are you sure your bottles aren't allowing CO2 to escape?