There are two things that really jump out to me in this video.
The first is that your un-engaged left fingers have a tendency to completely curl inward. This is usually a sign that your hand is being put under more tension than necessary. You may be relying on a squeezing technique to bring the string down, which will naturally result in a fist and some level of tension and flexing in the rest of the arm. This is very difficult to maintain and will become exhausting and potentially painful after more than a few minutes.
The much more disturbing thing I see (as in, that which disturbs your ability to play) is your position in relation to the bass. You have the bass set VERY high in relation to your seated height, and VERY vertical. The result is that the neck is much further away, both above and in front of you, than necessary.
Watch your video again and imagine the bass is not there. Watch how your body has to contort itself to reach the lower positions. Your left shoulder is raised well above your ribcage, and you have to stretch your arm around the neck. You're working way too hard.
Perhaps the best thing you could do at the moment is to experiment with your position. As a starting point, I would recommend lowering the endpin until the nut is about the same level as your left temple, and lean the bass back so the neck hovers perhaps 2-3 inches above your left shoulder, and 1-3 inches from the left side of your face. This would do a few things for you:
* Allows your shoulder to consistently rest on your ribcage without the need to raise it
* Allows your arm to dangle from the neck, which significantly reduces the amount of hand strength necessary to keep the string in the board
* Brings the neck much closer to your arm, which gives you far more flexibility to reach around to lower strings
* Makes thumb position much more accessible from a seated position
* Allows for an easy ear-to-neck pitch check you see so many professional orchestra players do
* Should also allow for better use of arm weight in the right arm if you lean forward slightly (though I realize that wasn't part of your question)
Paul you hit the nail on the head... again...

take as much of this as you can OP, it doesnt get any better.
Something tought to me was to avoid "Cell phone vibrato". What that is, if your vibrato sounds like your cell on vibrate, there is something wrong.
My suggestion is at this new height and technique focus on your left hand. Dont squeeze or press, let gravity take control.
Once you feel the lack of pressure you can start really working on it.

This exercise I attribute to Adam Hopkins, who helped me develop a vibrato that most in my studio are envious of. (and I know a few who would love to learn these techniques) With a few other tricks that will help your bowing at the same time I attribute to John Geggie/Hal Robinson bowings.
The Exercise: Vibrato Workout
Tools: Bass, Bow, Strings(ect.), Most importantly a metronome.
How to perform the exercise:
1.Set metronome to something comfortable, when I practice this I start at 50 and work my way to about 120-162. Lets say 50bpm
2. Place your finger on the string and start to do an exaggerated motion of the vibrato, vibrating on the quarter notes. This will help you get a feel for what vibrato should feel like and look like, you should do this for about 2 or 3 minutes
3. Stay at 50bpm and do eight notes, triplets and sixteenth notes. This is where it gets tricky, and much more difficult to do at higher speeds. Slow and steady. 2 or 3 minutes each.
4. Continue doing this at the same rate, when you get more comfortable add in bowings, my favorites: At eighth notes slur every 4 beats, at tripilets slur every 2 (yes 2), at 16th's every eighth. You can choose your combo's and such, however it is important not to go too fast you can hurt yourself.
5. add together and up the tempo.
6. Arguably the most important step in the entire process:
Listen to other bassists vibrato. Listen to what you like, listen to what you dont. Listen for times when
to vibrate and when
not to vibrate. Do you vibrate
more or
less in baroque music, do you vibrate
more or
less in Romantic music. Do I vibrate
more or
less when I want to get louder. Do I vibrate more or less depending on the theme: For example do I vibrate more in Koussevitzky's Chanson Triste and less in Humoresque? As a musician you need to be listening constantly, this is what is going to help you the most in your musical development.