Suggest me a 125 cc bike with style that would give me 50+ milage in city rides?

I'm a sales person so milage should be 50+… Don't suggest me Discover/pulser…
Does honda stunner cbf self start creates problem during winter?

Go for Honda shine
lovely little machine, silent, butter-smooth, reliable, and perfect for city conditions
a bajaj discover would do just fine, will give a better millage, but it has to be used more carefully and cautiously than Honda to make it last

If you want mileage blindly go for Honda Dream neo with HET mileage technology. Never goes below 60kmpl
It is 110cc but has great acceleration like 125cc

Hero ignitor or Yamaha SS125

Considering your requirements, you should go for the Honda CBF Stunner. It is a stylish 125cc bike that is sporty and offers a good mileage too. It is quite a reliable bike too.

Check out all details about the Honda CBF Stunner here: http://www.choosemybike.in/new-bikes/honda/cbf-stunner

Regarding the self-start issue in winter, most carburetted bikes, not just the CBF Stunner, take some time to start when it is cold. You will need to start it using the choke.

Bajaj discover!