Please tell me which is the best means of public transport to go from Bayswater to Stanstead airport? And how much time should we allow for this.

Do you mean Bayswater tube station - or just somewhere in the general Bayswater area? That could make a difference.

But in general -- walking to the Queensway station and then tube to Liverpool street station - 18-20 mins. Then Stansted express from Liverpool Street to the airport - every 15 mins and takes about 50 minutes. So all in all about 90+ minutes depending on wait time at Liverpool Street. ( A little longer if early AM or late evening because the S. Express runs less frequently )

Janis, thank you for your reply. It's very helpful to have this information in advance.

https://www.stanstedexpress.com/

look for special fares on the official site!