Although I drive, I still use lothian buses regularly to avoid parking in town or when on a night out. Lothian buses run an excellent service. A single ticket is £1.30 regardless of how far you travel, which is excellent value for me as I live about 40 mins out of town. The buses are always clean and reliable. The only problems I've had with late buses has been when there has been exceptional weather conditions or bad road works (or evil tram works). The buses even continued to run through heavy snow, albeit to a limited service and with diversions.
By far the best bit of lothian buses is the night bus service. There are regular buses throughout the night to all parts of the city and beyond. The night bus only costs £3 regardless of how far you go which is an amazing saving compared to a taxi. I regularly use the night buses and always feel very safe. And the drivers will drop me at the end of my street if I ask nicely enough.
Lothian buses are the way to travel around Edinburgh!