Maybe if you telephoned United and got a live person, the outcome might be different.

Considering that you paid a high price to have the bicycles accompany you, it is only fair the damage be reimbursed to you.

A year or so ago I had a problem with United concerning checked luggage. I called United and I was sent a $150 voucher for a future flight.

I was not required to return to the airport with the damaged bag to allow United to inspect the damage. The damage resulted from my bag being opened for "inspection" but in fact, it had been rifled while it was in transit.