There are a number of points to consider here.
It is possible to combine the 3 sites you mention into one journey, but it will take at least 5 days.
Day 1: Gondola lift from Borovets to Yastrebets, then walk over Musala to the 'Granchar' hut.
Day 2: 'Granchar' hut to 'Rilski Ezera' hut
Day 3: 'Rilski Ezera' hut to Rila Monastery
Day 4: Rila Monastery over Razdela saddle to 'Rilski Ezera' Hut
Day 5: 'Rilski Ezera' hut to Govedartsi of Panichishte
However, the big problem is that you want to do it in May. This route is certainly not safe or feasible in a normal May when snow will still be lying. In many places there will still be impassable snow-slopes over the summer paths and the only 'safe' route would be along the winter trails. However, these winter trails involve serious technical difficulties in places, and even then, are not designed for wet spring snow conditions.
So to sum up. if there is still snow on the mountain, which is almost certain in May, then I would not consider this route. I personally wouldnt contemplate such a route until late June at earliest, and even then late lying snow patches may cause problems.
If you are interested in walking in the Bulgarian mountains, then I suggest you take a look at the following book:'Walking in Bulgaria's National Parks':
http://www.amazon.co.uk/Walking-Bulgari ... 1852845740
It provides detailed route descriptions and background information on the best hikes in the Rila, Pirin and Central Balkan.