I found this bug (actually he found me) while walking through some bushes in the city (Iași, Romania). It is a small bug, a quarter of a fingernail, white and a fluff tail. He lays a white fluff on bushes (that is how I meet him, I brushed the bush and got the white fluff on me, when I wanted to clean it off I saw 2 moving on my shirt) and it seems they stay around it. I also found it near the plants, on a stone pavement, but I presume he got lost.
Based on the image and on the description, it could be a woolly aphid, a kind of insect that produces filaments of a waxy, cotton-like substance that gives them a fluffy appearance.
The images on Wikipedia aren't convincingly similar, but I found a better reference on abundantnature.com: