IMO. There are already some good advice and responses. Also, I am sure your teacher has good suggestions and knows you better than any one on this board, including me.
My bass tuba E-flat preference is the one I have had since 1988, a 3+1 1970 era Besson, with a 15-inch bell, and small shank lead pipe. I have found a Wick 4 or Wick 5 (small shank) works best because it helps with the a few flat notes above the staff as well as an added brightness that is closer to an F-tuba IMO. These tend to be rare when in very good/pretty condition. It is the brightest sounding e-flat I have tried, but not as bright compared to my MW2182 F-tuba. Each has advantages over the other depending on the music.
If I was currently looking for an e-flat, based on my taste that I mentioned above, and a limited budget, I would consider play testing these tubas. Hopefully you are located close enough to play test:
--Check out Dillon (NJ) selling a 15-inch Besson 3+1 with soft case for $2495 (
https://www.dillonmusic.com/used-besson ... 32195.html). As a caveat, you will need to get a small shank mouthpiece like a Wick (4, 5, 3). Older Bessons are made very well and built to last, but I would suggest you ask Matt Walters (at Dillons) what he thinks about the condition, including valve condition, and then decide with your teacher if it is worth a test.
--Consider looking for a used Yamaha 321 E-flat (4-inline top valve). I have known some past prominent players using the Yamaha 321 (15-inch bell non-comp) as a bass tuba in orchestra for some works as well as trombone doublers. I have seen these come up for a reasonable price maybe 3-4K, but am not sure about the market these days. For me, I still prefer the 3+1 Comp, but others may differ.
If the 15-inch bells sound too small for your taste maybe test these. However these might be getting in the upper budget range:
—Demo Eastman Model EBE853 Eb Tuba or used Besson 983 - Eastman seems to look to be a similar design to the 983. I never played an Eastman but liked the Besson when I tried one in 2002. I think Dillon had a good price on an Eastman Demo a few weeks back (Maybe 5-plus K??). Maybe a demo would fit the budget and worth a play test when/if they list a demo or have a deal on new. A used 983 e-flat price will depend on condition and seller. Both have a bigger bell (17) and likely a broader sound than a 15-inch, but the Yamaha 822 F-tuba is a larger F and maybe this E-flat might be closer to a bigger F sound you might favor (??). Others (repairmen, teacher, non sponsored owners) will have better knowledge about Eastman build quality than me, but I have heard Eastman are decent quality.