I don't bike commute but do ride and lift. Most lifting programs discourage cardio for a number of reasons but mostly because it almost always involves using your legs, which, if you exhaust them, makes it difficult to go heavy with squats and other leg intensive lifts. I don't believe this program discourages cardio per se but rather prefers you don't use cardio for warmup prior to lifting. I don't either but on cardio days, I do it after completing my lifts. But understand that beginning any new lifting program is going to result in stiff and sore muscles when you first start - it doesn't mean you are "shot." The health advantages of cardio are reinforced with each medical study; if your lifting program is not progressing as fast as you want, then modify it but don't give up the bike commute or even regular cardio. The 5x5 type program has been around a long time and there are many adaptations; it won't take you long to make adjustments to fit your goals and lifestyle.