Whishaw (1842) states that there were only two stations between Sheffield and Rotherham, Brightside (2 miles) and Holmes (4¼ miles). He does quite usefully give a list of all the planes between the termini, from which we see that Grimesthorpe Bridge (the actual bridge) was 138 chains from Sheffield. This agrees with what is shewn on the 1842 OS 6" map (courtesy of NLS).
In Midland days the Wicker terminus was 110 chains from Grimesthorpe Jn, which was at 162m42ch - which puts Grimesthorpe Bridge at 162m70ch by the Midland measurement.
The 1842 OS map ought to shew Grimesthorpe station but does not (it clearly marks Brightside and Holmes). However, just south of Grimesthorpe Bridge on the up side of the line is what looks like a short widening of the embankment with a flat area beside the line.
What sort of a station was Grimesthorpe Bridge? It never seems to have had a full service, and it never entered into the stations-banks of timetables, being always referred to in footnotes, as in this newspaper announcement of the service from 7 November 1842: "The 3 oClock Trains on Tuesdays, and the 4 oClock Trains on Saturdays, from Rotherham, and the last Trains from Sheffield on each of those Days stop at Grimesthorpe Bridgesame Fares as the Brightside Station." This is the sort of stopping-pattern (certain trains on certain days only) we know of for market services in many other places, but the times are wrong for that. Who was going to want to go into Sheffield in the later afternoons and come back late in the evenings (except for heavy drinkers, perhaps)? Anyway, I suspect that what this was was an extremely simple stopping-place on the embankment just south of the road-bridge, quite likely with no buildings. Although the road can still be identified easily enough, later expansion of railway facilities mean that no trace of the stopping-place could possibly remain.
The first reference to Grimesthorpe Bridge known to me is in Bradshaw for December 1841. It appears for the last time in the issue for January 1843, from which a closure-date of 1 February 1843 is derived. I do not know of any source for opening dates for any of the stations on the S&R line (which in this respect is one of the more problematic early lines), so the assumption I like others make is that trains may well have made at least some intermediate stops from the opening on 1 November 1838, which is the date generally cited for the stations.
