By default, Bridge checks automatically for new updates when
you click Publish wizard icon 
the first time of the working session with ArcGIS
Desktop®. If a new version is available, the GeoCat Bridge updater window is shown.
You can open this window manually by selecting menu Help / Check for updates or menu Tools / Options tab Updates/Support.
Click button Skip this version to ignore the new update. The next time you open ArcGIS Desktop® and click Publish wizard icon , if the version you have skipped still the latest one, you won’t be bothered. However you can change your mind and download the update by opening the Bridge updater window via the menu.
Click button Remind me later to close the window. You will be informed the next time you open ArcGIS Desktop® and click Publish wizard icon
Click button Install update to get the new version. When the downloading finished, a message box is shown:
When you close ArcGIS Desktop®, the installation will start.
If you are using the latest version, click the Check for updates will show the following message box:
Manual