What do you mean? You got bard as your main character or you are talking about Haer'dalis? If you speak of Haer'dalis, then no, his song does not improve, tho you can pick High Level Ability Improved Bard song, which is really nice, if you play as a subclass of bard - Skald - your song does improve as you level up.
Please use the search function. This question has been answered many times.
[font="Times New Roman"]“The world breaks every one and afterward many are strong at the broken places. But those that will not break it kills. It kills the very good and the very gentle and the very brave impartially.”[/font]