Losial Circuit
Wednesday Night Bike Track
Google Maps Location
Losail Photo

The Losail Ciruit is a Moto GP track located about 20 minute drive North of Doha. They frequently open for 'training days' on a Wednesday night from end of September until May each year where cyclists and runners have access to the 5.5km circuit. It is typically open from 5pm to 8.30pm. There is ample parking, toilets, showers and refreshment area.
Circuit
The specific days are listed on their website.

https://www.circuitlosail.com/events/training-days/

There are also female only training days.
https://www.circuitlosail.com/events/ladies-training-days-2018/

Losail Circuit Map