I want to address something else that concerns me. sewillis, you said you're holding down the pedal the whole time. If I understand you correctly, you are never even switching it? That is, you just keep it down? I don't know how new you are, but thought you should know that you pretty much should never do this.
In later pieces there are pedal markings in the piece, but in earlier pieces there aren't. However, if pedal is used, it should be switched generally when the chord changes. Sometimes it is down for an entire phrase, or other times it is changed every beat. There's a part in the concerto I'm learning where it's down for I think an entire measure of 32nd notes, because the sound is supposed to grow in sound to a pinnacle. So it all depends on the music and what the desired effect is.
Eventually, you have an intuitive feel for when pedal is needed or when it should be switched.
I've not played much Bach, but the pieces I've played by him I've not used much pedal at all. In the last piece I learned, the prelude to the second English Suite, there was only a little two-measure section before a the repeat where I used pedal, and also where I was a little more liberal with the rhythm.