Did he perhaps know the sculptor? As far as I know, the sculptor was active c 1840s to 1860s, in Dublin area, and also the son of a sculptor. Most sculptors seem to have been able to work with a few sittings and studies / reference .
It seems to be a pretty generic type of bust, with the "classical" drapery. There's a very similar bust of an Arthur Jacob.
If you can find family photos, or local press images( - he'd have had to be a fairly prominent citizen, to be worth having a bust made, wouldn't he? ) that might help assess how good a likeness it is even from other members of his family - an old sculptor I knew used to say as long as he got the ears right, he was okay, because people, especially family, always thought they'd been really observant spotting if the ears were correct, so the rest must be okay. (That chap worked in clay to be cast in bronze, though.)
Can't see it'd be all that different creating a sculpture ( subtracting to find the form within) than modelling (adding and manipulating, to build a form) given good skills observation and ability on the part of the artist, and he seems to have been very capable.
- Just realised I've repeated several other comments in part during this. Sorry.