Travel from London to Ireland -- bus / ferry?

Bus is a slower and less comfortable option than using a train.
All the rail + ferry options from London to Ireland are explained in this article by the Man in Seat 61: https://www.seat61.com/Ireland.htm
For London to Northern Ireland (Belfast) see this page: https://www.seat61.com/NorthernIreland.htm

Assuming that time has some value, I would prefer to fly.

What is your larger itinerary? Are you just wanting to get to Northern Ireland, or is something planned along the way? How long a trip is this? Long Weekend? 2 Months? Certainly Flying would be quickest and probably cheaper, but if you want to stop in Wales for example, then Bus or Train for part, depending on the location, maybe a combination of both.

Flying--it's cheap and the flights are so frequent that you will be able to suit your itinerary.

I'm puzzled as to why you want to crisscross the Irish Sea. Why not fly US-Dublin, travel on land from ROI to NI, then fly Belfast-Glasgow or Edinburgh and travel on land around Scotland and England, ending up in London?

I agree with the above post - if you haven't already booked your flights from the US, look into flying into the UK and out of Ireland, or vice versa, and save backtracking.

Also, if you are flying across the Irish Sea, you have lots of choices of airports. For instance, you could fly from Belfast City airport to Inverness or Aberdeen, so you could go right to northern Scotland, again saving backtracking (from southern to northern Scotland and than back south).

To learn which airlines fly where from an airport, look at that airport's Wikipedia page. Note that Belfast has two airports - City and International.

I did the London-Holyhead-Dun Laoghire train/ferry route and, while the experience was memorable, I swore next time I would fly. Ryanair can get you to Dublin pretty cheap.