One good thing that has happened in the past year in Bishkek is the installation of Free WiFi in many eating establishments. Check with the staff to see if WiFi is available in their premises for clients to use.
Places that I know have WiFi include Coffee (all 3 branches), Foyer, Obama, Cyclone, Pirogoff-Vodkin, Vostok Zapad, Tubeteika, Movie City Bar, Buddha Bar, Bellagio, Vanilla Sky, Coffee 135, Vefa Centre, Domino Rio, Arzu, Aroma cafe (all 4 locations), etc.
One thing is for certain, more cafes & restaurants will offer Free WiFi as part of their service to their customers!