The quick answer is that you can not retrieve the label that you give an Expression in a cycle group.
Typically the values in a cycle group are simply fields from the data model - and if these are named sensibly then GetCurrentField works fine. Often I will have a list of fields plus a 'No Grouping' option with an expression of =' '. I then display the caption as the following:
='Calculated Value' & if(mid(GetCurrentField([Cycle Group]), 1, 1) = '=', '', ' by ' & GetCurrentField([Cycle Group]))
This works as long as you only have a single calculated dimension.
If you have many calculated dimensions you could achieve the result you want by putting each expression into a variable and give the variable the name that you want to see. You can then use GetCurrentField but just strip out any characters from the variable name that you don't want.
='Calculated Value by ' & replace(replace(replace(GetCurrentField([Cycle Group]), '=',''), '[', ''), ']', '')
Hope that makes sense.