Can most bracelets be worn all the time including while showering or swimming?

You can but its better to keep Leather goods away from direct water contact. The more the moisture it comes in touch with, the lesser its life. It is better to keep them away from water to retain their best look & quality.

Answer #2: Answer #1 is basically dead-on but it should be noted that some leathers can safetly be in water without incurring any damage, such as leathers that were tanned using the "braining" process, which is tanning in somewhat liquified animal brain (In the field, this is accomplished by using the brain of the animal you skin). Leather tanned using this process is completely washable without being damaged. However, it's unlikely your bracelet was brained so it's best to keep it out of water, otherwise the leather will lose its finish and possibly become damaged due to excess moisture.