Not all vital records are available online and unless you have a date and location it can sometimes be difficult to find such records. Starting with Bridget's birth (hoping date in passenger manifests is correct)-
If she was born in Canada or U.S.- each province or state keep their own records and the starting date, information contained, etc. vary from one to another.
If she was born in Ireland her birth should appear online (Irish Genealogy) but if she was registered under another surname then without a location to narrow it down it won't be easy to find.
If Arthur and Bridget married in one of the 6 counties of Northern Ireland then it should appear in GRONI's database. If the marriage took place in the rest of Ireland then it should appear in LDS civil registration database (bride and groom listed separately so you need to cross-reference for matching details).
If marriage was in U.S. or Canada same problem as above- each province or state keep their own records and starting dates vary. Many have restrictions on what's available so there may not be even an index to check.
Regarding the deaths of Arthur and Bridget- if they died in N.I. more than 50 years ago should be in GRONI's database. If less than 50 years ago you will not find in online database.
The passenger manifest for "Marine Tiger" gives Arthur Loughlin's occupation as labourer not farmer.