How can I make my sourdough bread more sour?
I've just been dealing with a similar issue. My sourdough starter wasn't producing sour enough bread. In my case Russian black bread which is also rye. It was rising well but tasted like regular bread.

I did a some research and experimentation and fixed it.

I'm sure you are aware that a sourdough starter has both yeast and bacteria. The yeast consume sugar and produce CO2 and the bacteria consume sugar and produce acids including lactic and acetic. Acetic acid in particular (ie. vinegar) is very pungent and sour.

The type of bacteria you have will strongly affect the flavor and acidity of the bread.
After feeding, yeast is active early. As the acidity rises the yeast activity falls off and the bacteria become more active.
Yeast is also more active at cooler temperatures.

As your starter was bubbling well your yeast was obviously active. If it isn't sour then you either have mild tasting bacteria or they aren't active enough or both.

Several variables made a noticeable difference:  


I started keeping my starter in a warmer place.
It was early spring and my kitchen was cool. The yeast was active at those temperatures but the bacteria were very slow.
I introduced different flours.
I started feeding my starter with freshly ground wheat flour and rye. I was trying to get new microbes. The day after feeding with a new flour the starter changed flavor noticeably.  
I fed my starter less frequently
The recipe I was following said to feed the starter twice a day. This meant that my yeast was just finishing up their most active period when I fed again. The bacteria never really had a chance to take over. I read several articles that recommended leaving the starter a little longer and not feeding until the starter actually fell. The yeast weren't as active and the starter collapsed. After this point the starter would rise less but would become sour very quickly.


While I'm still not an expert, I found that I can now tweak these variables to tune my bread. If I feed more often and keep the starter cool it will rise more vigorously and be more mild. If I feed less often and in a warmer place then the bread will rise more slowly but be much more sour. I'm still trying to find a balance that I like but I know what variables to tweak.

The black bread I made this week was startlingly sour and delicious.

Addendum
I saw some blog posts that suggested that since the strongest flavored bacteria were producing acetic acid that one could simply add vinegar to the bread dough to achieve the same effect.
I tried it.
As you would expect it tasted sour but also flat and boring. I won't be cheating like that again.