There are changes in Bootstrap 3 that stops Google maps from displaying correctly in modals, or tabs.  New demos have been created to show to to utilize in your code.

Single Map: http://jenntesolin.com/demos/single-map_bootstrap3.html
Multi-Map: http://jenntesolin.com/demos/multi-map_bootstrap3.html

Download Code

To use in a tab, change the following:

$("#mapModal").on("shown.bs.modal", function () {

to

$("#mapTab").on("shown.bs.tab", function () {

Also, in the modal the "hide" class, as well as other changes as per Bootstrap Documentation.

Note:
This is an update to the older post using Bootstrap 2 with Google Maps.

Resources:
Google Maps in Navbar in Bootstrap 3
Bootstrap Documentation: V3
Bootstrap Documentation: Modals