If you’re cycling part-way, many stations on the Gatwick route have bike parking

https://www.scribd.com/document/1077066259/Heathrow-to-Gatwick-Airport-Transfers-Coach-Taxi-or-Train-174457

If you’re cycling part-way, many stations on the Gatwick route have bike parking. Leave your bike securely and continue by train to avoid busy airport road traffic.