I am trying to do Best of Bulgaria followed by Best of Greece & would like to know if anybody has done that connection & what type of transportation is available between the 2 cities.
Not the easiest border to cross. Rome2Rio.com is a good starting point when you're trying to answer a question like that. I've found its travel times, frequencies and fares to be way off base much of the time, but the website is generally pretty accurate about the existence of a particular type of transportation. Just keep clicking down through the website until you come to a link to the appropriate transportation company's website, where you should be able to get schedule information. Be very careful about days of the week, and Google to be sure you're not traveling on a national holiday.
Rome2Rio thinks a bus will be faster than a train, and it may well be correct. Trains are few and far between in that part of Europe, and they are not fast.
For flights I'd go to skyscanner.com
Non-stop flights take about 1 hour 20 minutes flying time, on 3 different airlines, depending on day of the week and time. Of course, extra time getting to and from the airports, etc.
You do not mention when the trip will be, but it appears there are 2-3 non stop flights per day between SOF-ATH, with prices under $50.
Use skyscanner.com, as noted earlier, and plug in your dates to see the options
PS-- it works better if you use the 'Sofia' spelling