Safe rate for increasing long rides
Is there anything specific you'd like to achieve or try while cycling? I cycle purely for fitness purposes and will cycle quite differently depending on available time as well as what I'd like to achieve in terms of strength or cardiovascular goals. As you're a runner, I'll assume you're well versed in gps devices like those by Garmin which will assist in tracking your efforts. 

I was able to increase fairly quickly from regular 10Km trips to once off trips off 30Km to 50Km to 80Km to 200 Km in the space of 1 month. Since then I've focused on better return for time in the saddle as opposed just worrying about distance covered. 

For my round trip commute of ~20Km, I will cycle pretty hard either on the way to work or on the way home which usually gives me a pretty good cardiovascular workout over ~20 minutes. For part of this I may go all out for 60-90 seconds. 

If I've got 1-2 hours available for a cycle then I'll either go for a 25-40Km flat route at 25-30Km/hr effort for cardiovascular training or a 15Km hilly route which will provide cardiovascular and strength training.

For long spins of 3+ hours I will try to cover mostly flat terrain with a couple of hills included and will aim for about 25Km/hr depending on weather conditions. 

As with any exercise, your nutrition and fluid intake before, during and after will be key in helping you maximise the return on your efforts.