I'm Bulgarian, we don't send cheap workers to EU. We have right to live and work in EU under the same conditions as everyone else in EU and a lot of Bulgarians happens to find employment in some EU countries under better conditions that they can find in Bulgaria and they go work there.
There's no an governmental institution in Bulgaria that collects Bulgarians from the streets and sending them to other countries to work work cheap, like they do with doctors in Cuba or workers in DPRK.
You find a job, get a plane ticket, go there and work, get paid like everyone else. That doesn't make you a cheap Bulgarian labor. They like to call it like that because the talent pool increases and they want to imagine that employers are hiring Bulgarian butchers that can't cut meat or Bulgarian developers that can't code just because its cheap. That's not the case, it's a free market.