From the documentation
How to position the tooltip - top | bottom | left | right | auto.
When "auto" is specified, it will dynamically reorient the tooltip. For example, if placement is "auto left", the tooltip will display to the left when possible, otherwise it will display right.
Example:
<button class="btn btn-default" title="" data-placement="right"
data-toggle="tooltip" type="button" data-original-title="Tooltip on right"></button>