How do you commute on a bicycle in Dubai?

The best way to find the answer to your question is to find cycling clubs or cycling community near you. I googled "cyclist in dubai" and found this club:

Rides and Clubs - Dubai Cyclist

If you can tolerate the summer temperature of 40-50 Celcius, I am sure that club members who are already cycling in Dubai should be able to give you some tips of what you should and should not do while cycling in Dubai.

If you don’t like the idea of joining a club, you can read about “Cycle laws and safety in Dubai and UAE” at Cycling in Dubai. That is where I discovered that cycling is not allowed on major highways and motorways and there are no bike lanes. So, if you are concern that cycling on roads in Dubai is not safe, consider cycling in the desert. That should be a great way to work out for fitness.

If you are thinking of cycling in the desert, a fatbike is what you should consider cycling on because it can handle sandy, muddy, grassy and rough terrain well.

Here is what it is like cycling on sandy places like the desert.
https://youtu.be/grZ-LL6NOgI