Carolyn,
The Freeholder Lists are lists of those with a vote. To be eligible to vote in the later 1700s you needed to be male, have land of above a certain value (£2 rental per year) and, until 1792 be Protestant. Only a tiny percentage of the population had that amount of land (less than 5%) so though useful if you had family with land, the vast majority of migrants families won’t be listed in the Freeholders lists.
If Bernard went to Scotland to work in the mines, then that economic profile indicates to me he almost certainly came from a labouring/weaving background and not that of comparatively well off farmers, so you wouldn’t expect to find them in the freeholder lists. Nor would you expect to find him in the O’Neill estate records at PRONI that I mentioned previously. They list all the farmers townland by townland, but the agricultural labourers and weavers are not listed there. (They sublet from the farmers and not from the O’Neills) and in general no records exist for them for the late 1700s and early 1800s.
Regarding Bernard’s religious denomination, I’d be very surprised if he wasn’t RC. It’s a forename mostly only found in RC families in Ireland. I looked at the 1901 census for Ireland. There are 17,213 people named Bernard. 16,843 are RC.
There were very few passenger lists for migrants from the UK to Canada before 1850 (the authorities in Canada didn’t need them) so if Bernard’s family migrated from Scotland to Nova Scotia c 1841 there probably won’t be a passenger list to locate. There were separate sailings from Glasgow and from Liverpool. I haven’t come across many vessels that went from Liverpool to Glasgow and then on to Canada. Vessels from Liverpool and Glasgow did however often stop in Ireland, especially in Moville, in Co Donegal to pick up extra passengers. But if he was living in Scotland, I’d just expect him to have sailed directly from there.
Regarding Scottish mining records, you can try this website:
http://nationalminingmuseum.com
Regarding mining in Ireland, by and large there wasn’t any, that’s why people went to Scotland or England to work instead. Ireland has very few natural resources, a key factor in emigration for over 200 years. Therefore it didn’t benefit from the industrial revolution and so people had to leave and go to where there was work. With the exception of very small quantities of coal along the Antrim coast and some in the Leitrim area there isn’t any coal in Ireland. There was also tiny amounts of mining for iron ore and the like but these employed very small numbers. So hardly any miners in Ireland. In contrast, Scotland and England is/was full of coal, so tens of thousands of Irish labourers went there to work. (But, in general, they would not have been miners in Ireland. They would have learned the trade in Britain.).