I can’t really speak for all Bulgarians, but in general our opinion about Turkey is “KILL IT! KILL IT WITH FIRE!”, especially now under Erdogan (and needless to say – especially for our ultra-nationalists). Of course, that doesn’t stop many common people from going there on holidays or for housewives to watch Turkish soap operas (as Gaius mentioned). And all this probably leads to a better opinion about the people themselves rather than the country. Not to mention the Bulgarian Turks – our ultra-nationalists probably hate them as well (though enemy №1 are obviously still the Gypsies), but I think the general populace is quite ok with them – I personally see them mostly as quite hard-working and honest people. Still, the image of Turkey as a country, as an idea, still carries a horrible load from the past.
As for Georgia – we don’t think or hear much about them. Those who are especially Russophilic might dislike them and those with an interest in medieval history would connect them with the Bachkovo monastery, but other than that I can’t think of any connections or images we as a whole would have of Georgia.