I am queen of laziness, and I have to use AnyConnect, and that screws with Docker, and then I have to go looking to remember the magic incantation to get things right...

Who has time for that?

I made a script that wraps the whole thing up and reminds me what I should do when it doesn't work.

Instead of:
> docker-machine env default
I do this instead, and the script does the rest:
> . dockerEnv

The contents of the script are pretty trivial (I am sure shell wizards can find plenty wrong with it, starting with the direct reference to bash, but whatever. Laziness, right?):

#!/bin/bash
UP=`docker-machine status default`
if [ "$UP" != "Running" ] ; then
    echo "Starting default docker VM"
    docker-machine start default
fi

eval "$(docker-machine env default)"
export DM_IP=$(docker-machine ip default)
echo $DM_IP

DM_SUBNET=192.168.$(echo $DM_IP| cut -d'.' -f 3)
RESULT=`netstat -rn | grep $DM_SUBNET | grep vboxnet`
if [ "$RESULT" = "" ] ; then
    echo "Adding route for vboxnet0"
    sudo route -nv add -net $DM_SUBNET -interface vboxnet0
    RESULT=`netstat -rn | grep $DM_SUBNET | grep vboxnet`
    if [ $RESULT = "" ] ; then
        echo "Quit AnyConnect and re-run this script."
        exit
    fi
fi
docker-machine ls

[edit on 3 Sept: updated for even better-ness. Laziness rocks.]