For this all you would need is tunneling/port forwarding from vagrant to mysql.
Being on vagrant machine, figure out what the host ip is, usually netstat would tell you that.
The default being 10.0.2.2 and assuming you have 3306 port on host machine do the following
ssh email@example.com -L 3306:127.0.0.1:3306 -N
The above would forward the 3306 [ the one on the left ] to the hosts port. Mind you, you have to use 127.0.0.1 to access your vagrant machine in place of localhost which might not work.