I don't know who you are flying but usually if you are over the dimensional limit, the weight allowance goes to 70 lbs. My bike bag always weighs under 50 lbs and if I get "caught" bringing a bike, I say it weighs less than 50 lbs and is less than 158 cm. The Agent is usually confused by the following langauge on United's site. I did not have to pay either direction on my last trip although it took some discussion on the way home.
I am flying to Paris on United and basically accept that it is going to cost me 2 hundred smackers but that gets me 70 lbs on the bike bag. On the return, Air Canada will be free.
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 $150 USD/CAD service charge applies each way for travel between the U.S., Canada, Puerto Rico and the U.S. Virgin Islands, and a $200 USD/CAD 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