All ascending divers will have bubbles.
Even non divers on the surface can have bubbles caused by cavitations as joints move around.
The key is how your bubbles are managed.
Bubbles form when the pressure of nitrogen in solution exceeds, by a certain amount, the ambient pressure. The extra amount of pressure above ambient required to form a bubble (leading to a state of 'supersaturation') is because the growing bubble needs to overcome both ambient pressure and the surface tension of the bubbles 'skin'.
Small bubbles have higher surface tensions than larger ones, so small bubbles need a higher internal pressure to form and grow compared to larger bubbles.
If you looked at your blood under a microscope as you ascend you would see millions of microscopic bubbles form, and just as quickly redissolve. You would also see a much smaller number of larger bubbles hanging around that are stable, due to their lower surface tension, and lower internal pressure.
The key is to maintain a pressure so that all those millions of small bubbles keep redissolving and you keep only a few larger bubbles. This allows you to transport the gas to your lungs, where the 'supersaturated' gas can escape.
If you ascend too quick for the tissue and blood to transport the dissolved gas to your lungs then all those small bubbles have a chance to grow to a size (a 'critical radius') where they become stable - and can then go on to grow to the point that they can do damage: leading to DCI and/or foam for blood.
Cheers,
Rohan.