To initiate bulk selection in the conversation list, hover over the timestamp on one of the conversations and then check the box that appears on the right side.
Once selected, a menu will appear to the left to take action to the select conversation(s). You can select all of the visible conversations that have been loaded in the list. To select all, initiate bulk selection mode on one of the conversations and then click "Select all shown" in the center of the page.
Once done, you can then choose any of the actions listed to apply to those conversations.