Men get all of the glory, at least in most histories until fairly recent times. I recently came into posession of a 1787 Edinburgh edition of Burns, the second edition in the world (Belfast was the third edition, later that same year – however, it was a 'bootleg' edition – the London edition formally claimed the title of being the third edition on its own title page). In an early form of 'crowdsourcing', people would place advance orders with the printer, and their names would appear in the eventual book as a subscribers list. In this Edinburgh edition there is just one name which is identifiably from Ireland - the Countess of Moira. Her address is given as 'Montalta, Ireland' - which is of course Montalto House in Ballynahinch.
Elizabeth Rawdon (1731–1808) had been born in England, had multiple titles, but came to Ulster in 1752 when she married John Rawdon, the 1st Earl of Moira, becoming his third wife. She was a literary patron and antiquarian. She ordered 6 copies of Burns' second edition.
11 years later in 1798, the Battle of Ballynahinch took place at Windmill Hill which (from memory) is within the grounds of or certainly very close to Montalto estate. Presumably the Countess watched from the safety of the big house, possibly reading one of her 1787 Burns volumes, probably struggling with unfamiliar vocabulary, while the muskets cracked, pikes clashed and blood flowed a few fields away. Earlier this year the estate hosted a Country Fair which included a re-enactment of the battle.
Others more knowledgable than I will know whether this is the first confirmed link between Burns and Ulster. The subscribers list shows just how much the 'Ploughman Poet' was admired, and supported, by the gentry. In the 1600s, George Rawdon was one of the most notorious opponents and persecutors of the Ulster-Scots Presbyterians.
The last image is of the Country Fair & battle re-enactment publicity, and is from this website.