United's "official" rules on bicycles: (Note that I have been able to break a bicycle down small enough to fit in a box that was "legal" and thus had no surcharge.

****
United accepts non-motorized bicycles with single or double seats (including tandem) or up to two non-motorized bicycles packed in one case as checked baggage. If the bicycle(s) are packed in a container that is over 50 pounds (23 kg) and/or 62 (158 cm) total linear inches (L + W + H), a $100 service charge applies each way for travel between the U.S., Canada, Puerto Rico and the U.S. Virgin Islands, and a $200 service charge applies each way for all other travel. If the bicycle(s) are packed in a container that is less than 50 pounds (23 kg) and 62 (158 cm) total linear inches (L + W + H), there is no bicycle service charge, but the first or second checked bag service charges may apply.

The following are bicycle restrictions:

Handlebars must be fixed sideways and pedals removed, or
All loose items must be enclosed in plastic foam or similar protective material, or
Bicycle should be transported in a sealed box. If a box is needed, see the Courtesy Bags section of this site.
If your itinerary includes a United Express flight, please contact United for information regarding aircraft cargo hold limits
United is not liable for damage to bicycles that do not have the handlebars fixed sideways and pedals removed, handlebars and pedals encased in plastic foam or similar material, or bicycles not contained in a cardboard containers or hard-sided cases.
Note: Bicycles will not be accepted during an excess baggage embargo when no excess baggage is allowed.

****