Size of BarLegend

Here's a workaround that might help others in the future: do not use BarLegend and create your own bar using DensityPlot. This way one gets the ImagePadding option.

Here's an example that works perfectly.

Horizontal bar legend

myBarPlot = 
 DensityPlot[x, {x, -1, 1}, {y, -1, 1}, 
  PlotRange -> {{-1, 1}, {-1, 1}}, ColorFunction -> "SunsetColors", 
  AspectRatio -> 1/15, FrameTicks -> {{None, None}, {True, None}}, 
  ImagePadding -> {{50, 8}, {20, 2}}, ImageSize -> 300];

Column[{myBarPlot, 
  DensityPlot[Sin[x y], {x, -Pi, Pi}, {y, -Pi, Pi}, ImageSize -> 300, 
   ColorFunction -> "SunsetColors", 
   ImagePadding -> {{50, 8}, {2, 2}}]}, Spacings -> 0]

Vertical bar legend Second case, suggested by @OkkesDulgerci

myBarPlotVertical = 
 DensityPlot[y, {x, -1, 1}, {y, -1, 1}, 
  PlotRange -> {{-1, 1}, {-1, 1}}, ColorFunction -> "SunsetColors", 
  AspectRatio -> 15, FrameTicks -> {{None, All}, {None, None}}, 
  ImagePadding -> {{2, 25}, {5, 5}}, ImageSize -> {Automatic, 300}];

Row[{DensityPlot[Sin[x y], {x, -Pi, Pi}, {y, -Pi, Pi}, 
   ImageSize -> {Automatic, 300}, ColorFunction -> "SunsetColors", 
   ImagePadding -> {{50, 8}, {5, 5}}, PlotRangePadding -> None], 
  myBarPlotVertical}]

Still, would be great to know, if there's an "official" way to do it using BarLegend.

You gave a good answer. However, in addition to that, here is the one based on using the standard technique:

DensityPlot[Sin[x y], {x, -Pi, Pi}, {y, -Pi, Pi}, ImageSize -> 300, 
 ImagePadding -> {{50, 2}, {2, 2}}, ColorFunction -> "SunsetColors", 
 PlotLegends -> 
  Placed[Row[{Spacer[30], 
     BarLegend[{"SunsetColors", {-1, 1}}, LegendLayout -> "Row", 
      LegendMarkerSize -> 300 - 26]}], {Above, Center}]]

One can play with two parameters to adjust the size and position: (1) the argument of the Spacer as well as with (2) the value of the LegendMarkerSize.

Have fun!