Traveling Bath to Pimlico

The National Express bus is by far the most sensible. Pretty much anywhere in Pimlico is walkable from Victoria Coach Station.
Or taxi or a short London bus ride from straight outside the coach station.
The service is almost every hour, and advance fares start from just £5.

(Not all services call at Heathrow, hence the greater frequency to London, as opposed to Heathrow)

From Paddington just take the circle line counter clockwise 7 stops to Victoria. It may or may not be worth changing 1 stop at Victoria onto the Victoria line to Pimlico station.

The train takes half the time of the bus, is twice an hour and costs from £23 booking in advance.

So it's all personal preference.

If going via Paddington you can avoid one flight of stairs if you walk up the slope to be outside the main station, cross Praed Street, and enter the Underground from there.