The curly braces are inside the string, so it is being evaluated as string. They need to be outside, so this should work:
<div className={"btn-group pull-right " + (this.props.showBulkActions ? 'show' : 'hidden')}>
Note the space after “pull-right”. You don’t want to accidentally provide the class “pull-rightshow” instead of “pull-right show”. Also the parentheses needs to be there.