I know that when using gem install, the gem will be stored under /home/username/.rvm/gems/, under which gemset the gem was installed.
But if I use Bundler and specify the gem in the Gemfile, when I run bundle install, where will those gems be stored? And what if I already installed the gem using gem install, if I run bundle install, will it use the previous gem installed using gem install?
It depends. In the usual development setup they are installed where they would be when you install a gem "normally" (by running gem install foo) and bundler won't reinstall gems that are already there. This location depends on how rubygems itself is configured.
If you run bundle install with the --deployment option then the gems will be installed in a location unique to your app (you can pass this as a separate option but it defaults to vendor/bundle)
You can also run bundle package to store all the .gem files your app uses in vendor/cache. Running bundle install will prefer gems in vendor/cache to gems in other locations.