Your sprained ankle could certainly have an adverse affect on your back because if you alter your gait you will put altered and abnormal stresses on your spine. A bulging disc can cause all kinds of problems--the outer layer of the disc is pain sensitive and can, all by itself, refer pain into the leg. Also if the disc is bulging it will also have lost some height bringing the small joints of the spine into closer proximity and jamming them together, restricting normal movement. You have probably developed 1 or 2 stiff segments by now which would tend to seize up if you sit for a long time causing pain and also causing poor nutrition to the disc. Have you tried looking into McKenzie techniques as suggested by a previous correspondent? Check out this link which shows a simple McKenzie technique for reducing a disc bulge. YouTube - How To Exercise With A Disc Bulge If you follow this link to the McKenzie Institute and click on "products" you will find a further link to a book by Robin McKenzie called Treat Your Own Back The McKenzie Institute (UK) Trust Website . My other suggestion is to look into Sarah Key treatment methods. Follow this link to the Sarah Key website (she is an Australian physiotherapist) Sarah Key and read "Your Back Pain" then click on th left hand link "The Back Block Video" in which Sarah Key herself talks about the Lumbar spine and demonstrates the use of a back block.
As a physiotherapist I tend to use a combination of these 2 methods depending on the individual patient, along with manual mobilisations (hands on stuff) and have found them very successful.
Kind regards
Suzy