I switched from tenor trombone to bass about a year ago, and ever since then my tone (especially in notes above middle C) has not been very good. Additionally, playing fast articulations, such as Hungarian March, has been very difficult. How can I practice to be better at these two things?
When switching from an 8.5" bell (or smaller) to a 9.5" (or larger) bell, as one does when switching from tenor to bass trombone, the sound will become significantly different to the players' ear though it is often much more similar to their prior sound than this feedback gives. So your articulations and tone are perhaps not as poor as you think they are.
That said, you are on different equipment, and different equipment also may require a different embouchure. This is highly individualized, and be weary of any teacher who offers a "one-size fits all" approach to equipment or playing. "All embouchures should be 50/50 upper-lower ratio, and centered left to right." Or "you're playing on too [big/small/shallow/deep/open/wide/narrow] of a mouthpiece, only people like Alessi and Yeo can play on [coffee cups/toilet bowls/bird baths/tuba on a stick/trumpet on a stick/etc.] size. Which isn't to say you are necessarily doing the right thing or playing the right thing, but much can be done to hinder even with the right intensions.
It is difficult to provide assistance over the internet, particularly with no other input to go off of. I will say that if I were going to be doing a self-diagnostic, I would use Sam Burtis's book "Time, Balance, and Connections", which is a modified Caruso method. In particular, one exercise from it that I find to be of particular merit is playing intervals, arpeggios, and scales without removing the mouthpiece from my lips. At all. Even going so far as to breathe through the nose for this exercise. The best I've found for working on range is like this:
(Bb Major) Bb C Bb | C D C | D Eb D |etc. Playing the scale as such, through as many octaves as I can. If I can only hit a high D, I'd stop there, reset the embouchure and continue playing. Don't remove the mouthpiece until you cannot physically play notes, but at the same time, don't do anything that will cause injury. If you experience pain or anything beyond mild discomfort, stop. You will feel some discomfort, especially if you're accustomed to switching between 5 - 6 embouchures. Most of my high school students have at least 6 embouchrues, even if they initially said they only have "one" embouchure. This is called a connection exercise, and the goal is to bridge as much of your range as possible.
Beyond that, I'm a student of Doug Elliott, who also makes mouthpieces. He has been an excellent resource for me, and is happy to help set you up with a piece that works best for your particular embouchure. I, as well as many others, do well with a disproportionately large rim but modest size cup across all instruments. From tuba to alto trombone. Others work best with relatively small equipment on each instrument. And every permutation in between. Taking a Skype lesson with him, or anyone else who has a history of turning out successful students is very prudent, even if for 1 - 5 lessons over the course of many months or years. The greats are not as expensive as you'd think, and are often very open to teaching students of any ability so long as they are committed to learning.