The bounding box uses the defined glyph box of the font as a minimum size. If the glyph box, as designated in the internal font information, contains extra space, the bounding box can't be made to ignore that.
You can use some trickery though, without converting to outlines.
In the Preferences > General, tick the "Use Preview Bounds". Then select the text object and choose
Effect > Path > Outline Object. This effect won't cause any noticeable visible difference in the type but will cause the area type box/bounding box to use the visible area as a basis for its size.
Once things are aligned, you can untick the Preview Bounds preference again if it gets in the way (it can at times). You'll see the extra space again, but it shouldn't matter after you've already aligned things - the position of the object won't change if you turn off the Preview Bounds pref after aligning. (You could also remove the Effect after aligning if desired.)
Of course, you could also use Point Type rather than Area Type in many instances.
Possibly related: Align text in exact center (vertically and horizontally) without creating outlines?