u know that whole on the first key, and how theres a bottom part to that key? well u slide ur first finger below and uncover the whole and play the clarinet altissimo fingerings. They're all the same (for the most part) 'cept u have to uncover that whole but press the key down.
I had this problem when I first started on bass. I overcame it by changing to a harder reed, from #2 to #3 , by strengthening my embouchure and by raising my head slightly so that the mouthpiece pointed more downwards. Try it and let us know how you get on.
I'm having the same issue. Have another bass clarinetist try out your horn with their mouthpiece. Often times, it's actually the instrument- minor leaks that wouldn't be a problem on soprano but are a big issue on bass. Both of the school instruments given to me had that problem, so if you are using a used instrument that could be a factor.
They are difficult to play even on a working instrument, though, so after checking to make sure it is your problem, try some scales and octave slurs. Octave slurs are where you play a note like low E, then apply the register key. Move up this exercise and try to hit the notes you're having trouble with. DO NOT change your embouchure or mouth when trying to play the high notes, just change fingers. Especially don't bite down.
It all ddepends on what the make and model of your bass clarinet is, and what mouthpiece you are using. Does your instrument have one or two register vents ? If only one you can certainly have trouble with the upper half of the clarion register. Let us know the details of your instrument.