We use buses or trolley buses the most. During the winter we used taxis a bit - coming from a hot country we found the slippery ice quite a challenge.
Fares a bus 6 com
   a trolley bus 5 com
   a taxi 70 - 100 com
   a mashrutka (minibus) 8 com (We find these a bit of a challenge and not worth the effort.)
We use the first two mostly.
Safe? From a personal perspective certainly - anyone from old ladies to single women or families with children can feel secure. From a road safety perspective? Today the bus driver changed lanes, took our fares and moved over to drop us off, all while using his hand held mobile phone. But we got off safe and sound. Safety is all relative, isn't it?
There isn't a schedule for any of the public transport - just wait till something arrives! You learn to factor that into a journey.
But coming from a country where public transport is virtually unusable - this is a pleasure. We can get from A to B with relative ease and we are enjoying our time in Kyrgyzstan.