My skin gets too dry if I shower more than once a day. Would that cause bacterial infections?

No. Dry skin itself does not cause bacterial infection. In fact, in your case by taking shower daily, you are likely reducing risk of bacterial infection. Many people have the dry skin, after taking shower, particularly in winter. You should apply lubricant such as petroleum jelly, or vaseline to the skin to protect breakdown of the skin. Once the skin breaks down, it does increase the infection risk.