Fewer, Michael. 1996. The Way-marked Trails of Ireland. Gill & Macmillan  
See Chapter 3, The Barrow Way. This twenty two page chapter describes a 126 km walk along canal and river tow paths from Robertstown on the Grand Canal to St. Mullins. The walk is divided into seven sections varying in length from 11.2 km to 22.5 km with estimated walking times varying from 2.75 hrs to 5.5 hrs. 

See also the descriptions of walks along the Barrow Line by Kenny et al. The Guide to the Barrow Navigation of Ireland published by Dúchas includes maps that show the Barrow Way. The text adds little additional value for the walker.

Further information is available on the attractive Bagenalstown Festival web site.
 

Other suggestions

1. Borris and the Mountain River. Preliminary research suggests that it may be possible to walk from Borris Lock (S718495) or Ballingrane Lock (S734478) along the towpath to the confluence with the Mountain River and from there to Borris.
    
2. Brandon Hill. A review of Map 68 will suggest a number of walks from Graiguenamanagh (S707438) to Brandon Hill (S697403). Possibilities include walks to the top and around the hill.
    

Maps:
Ordnance Survey of Ireland, Discovery Series 1:50,000
- Map 49, Lowtown to south of 22nd lock
- Map 55, From north of Rathangan to south of Athy
- Map 61, From south of Athy to south of Muine Bheag
- Map 68, Barrow River from south of Muine Bheag
                 to confluence with River Nore
- Map 76, River Barrow from confluence with River Nore to the sea

See also: Guide to the Barrow Navigation of Ireland
 

The IWAI Publications page references a number of books that include material about the Barrow River and Barrow Line. These include significantly more information than is contained in the sources cited on this page all of which focus on walking.