Bat seen flying over stream around midday, seemed larger than a pipistrelle, broad wings, steady flight.
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I don't think that you'd be able to identify a bat from these photos and the behaviour. The only bat that appears to have broader wings in flight is a Brown long eared bat ( and that's only if you have a good eye!). BLE's do fly above and near water too, like most bat species. But I wouldn't like to guess what this is.
I thought it probably wouldn't be enough for an ID.
Lat/Lng: 57.07056, -3.99899
OS grid ref: NN788994
River Tromie not far from Tromie Bridge.