How Can JPEG Be Used to Realize a Transfer Application with a Fixed Bit Rate?
You calculated the needed compression ratio correctly.
Now to answer the rest of the question:


The JPEG Algorithm doesn't let you set the size of the output file only the Quality measure. Namely to ensure the size of the output is close to the limit (Namely highest quality) requires trial and error (Though using the Quality you can get a measure of the bits per color).
The JPEG 2000 on the other hand allows you to cut the data at the exact number of bytes required hence makes the task much simpler (You can practically set a threshold on the output size).
The image quality of JPEG at compression ratio of ~100 is really bad (See Wikipedia article on JPEG). While JPEG 2000 can get better results.


To understand the Quality in JPEG, have a look at How JPG Works by Colt McAnlis:



Pay attention to the line:


  Probably most important, is that the quality parameter varies depending on the image. Since each image is unique, and presents different types of visual artifacts, the Q value will be unique as well.


This is what JPEG 2000 makes easier.