Hi Bill,
Each version contains all the files necessary to be run, you don't need to install interim versions. You can directly install the last version (3.1.301).
More information can be found on the documentation, page 23.
Please note that when upgrading BIDS from version 3.1.247 or less, it may be necessary to reenter your license key and your SPLogin credentials if it was configured.
Regards,
Marien Monnier
Enesys