Would walking cause an annual tear or bulging disc in the low back to be worse or cause pain?

Unusual: We often try to discern cause and effect to understand how injuries occur, but standard walking does not cause annular tearing or protrusion of discs. However, once present, the gravity effect of prolonged standing or walking, and the jostling on uneven ground can result in exacerbation of the symptoms.

Not necessarily: Not necessarily. The biomechanical stress on the intervertebral disc is greatest when sitting not standing/walking. When walking makes things worse i suspect other factors such as facet joint disease, obesity, or muscular pain from deconditioning/sedentary lifestyle.