Instead of constantly typing the full path when using the cd command, BASH has a built-in feature called CDPATH. Thanks to lhunath who explained in this SO Post how to use this feature.

The first time you do this, you need to create a hidden folder and add CDPATH to your bashrc (note this step only needs to be done once):

mkdir ~/.paths
cd ~/.paths
echo 'CDPATH=~/.paths' >> ~/.bashrc

Then to add symbolic links use:

ln -s /my/very/long/path/name/to/my/project project
ln -s /some/other/very/long/path/to/my/backups backups
echo 'CDPATH=~/.paths' >> ~/.bashrc

To update your bashrc:

source ~/.bashrc

Now you can enter the folders from anywhere by simply typing

cd projects
cd backups