The Encyclopaedia Britannica takes the figurine of the Roman soldier bagpipe player as evidence of the utriculus (or bag) bagpipe in England in Roman times.
Roman bagpipes were of the utriculus (tibia utricularis or pipe with bag) type. One image shows paired chanters and a drone. The reservoir is not known before the Roman examples. The Romans (and their Greek contemporaries in Egypt) were musically sophistocated, having invented the hydraulus, the direct ancestor of the pipe organ. Suetonius (ca. 69-140 AD) described the Roman instrument. The instrument with bag also is shown on Roman coins. Anything before then is speculative- pipes but no bag.

One website discussion suggests that the bagpipe came to England with Celts before the Romans, but this is just wishful (hopeful? wistful?) thinking on the part of some Scot or Irishman. No evidence whatsoever.

The Oxford History of Music discusses bagpipes(?) shown on a Hittite slab, ca. 1000 BC. (haven't seen the image, but doubt that there was a bag). I can't find any evidence that the Persians had real bagpipes, although mention is made in the Encyclopaedia Britannica.

The bagpipe from India is known as a mushug- no idea of construction.