How to make the bar be a button?

You can wrap input data with Button with action CopyToClipboard:

data = {1, 2, 3};
BarChart[Button[Tooltip[#, "I want tip"], CopyToClipboard@#] & /@ data, 
  ChartElementFunction -> "GlassRectangle", ChartStyle -> "Pastel"]

Update: You can add tool tips in several ways:

tooltips = {"tooltip1", "tooltip2", "tooltip3"};

1. Use Tooltip as a wrapper on input data:

BarChart[Button[Tooltip@##, CopyToClipboard[#]] & @@@ 
  Transpose[{{1, 2, 3}, tooltips}],
 ChartElementFunction -> "GlassRectangle", ChartStyle -> "Pastel"]

2. Use Placed[tooltips, Tooltip] as the setting for the option ChartLabels:

BarChart[Button[#, CopyToClipboard[#]] & /@ data,
 ChartElementFunction -> "GlassRectangle", ChartStyle -> "Pastel",
 ChartLabels -> Placed[tooltips, Tooltip]]

3. Use a custom ChartElementFunction and pass the tooltips as metadata:

ceF[cedf_: "GlassRectangle"] := Button[Tooltip[ChartElementData[cedf][##], #3[[1]]], 
BarChart[Thread[data -> tooltips], ChartElementFunction -> ceF[], 
 ChartStyle -> "Pastel", PlotLabel -> (Paste[])]

This is to get a slightly modified version of kglr's comments recorded as an answer. The modification is provide individual tooltips for each bar.

BarChart[
  MapThread[
    Button[Tooltip[#1, #2], CopyToClipboard@#1] &,
    {{1, 2, 3}, {"left", "mid", "right"}}], 
 ChartElementFunction -> "GlassRectangle", ChartStyle -> "Pastel"]

.1

Also, be aware that if only want the tooltip to show the value of the bar, you don't need to specify Tooltip; it will be supplied automatically.

BarChart[Button[#, CopyToClipboard@#] & /@ {1, 2, 3}, 
  ChartElementFunction -> "GlassRectangle", ChartStyle -> "Pastel"]