It is believed it was in Scotland but it actually didn't become popular there until around the 15th Century. It is though believed Emperor Nero played something not dissimilar to the bag pipes and the Romans played the Tibia Utricularis made from the tibia of a human skeleton. The allos is more like the bagpipes though as it had more pipes like the ones we know today.

So it is said they are of Roman descent not of Scottish origin.

http://www.bears.co.nz/dyk/bagpipes.htm

I did read somewhere (sorry I can't remember where) that they were invented by the Hittites. They lived in Anatolia before the Turks invaded it.

the scottish bag pipes we use today are actually a cover of the indian bag pipes the roman ones were more like the irish pipes