I looked at the prices of bike rentals and it seems to be in the $60-75 ballpark per day. I would be doing this for a two week rental.
United says
this - I also posted it below. The big factor seems to be the size of the case, 62 total linear inches seems to be well below a typical bike case, so I would have to pay $150 each way. I will call them though to confirm. $300 is still cheaper than renting a road bike that may or may not fit me (I will likely need a super small) for two weeks.
We will have a rental car at the airport, but at some point will still need to transport the bike and the case from hotel to hotel.
United Airlines Policy
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 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 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.