بسم الله الرحمن الرحيم
As many things are sold and purchased on auction day and night, in the same way it is lawful to buy or sell bike on auction as well. If you have any doubt or objection then write it clearly and submit your question again.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.