As a Certified Chiropractic Sports Practitioner and FasCat Athlete who has also suffered disc bulges I can tell you YES, you can resolve this problem and get back to long hard bike rides!
Technically a “bulge” isn’t as serious a diagnosis as a “herniation” which is less serious than an “extrusion or protrusion”. Anyway, 95% of disc bulges slip posteriorly which results in an ‘extension bias’. That means back extension makes it feel better and flexion (as in bending at the waist to reach the handlebars) feels worse! So, yeah, it totally sucks to get this injury as a cyclist.
If you’ve seen a PT, they probably prescribed and coached you through “McKenzie Positioning” exercises. If you saw a good chiropractor, hopefully they did some decompression treatment. Once the radiating pain is resolved and you can bend forward without incident, you’re officially sub-acute or even resolved.
BUT - you are more susceptible to this problem in the future. If low back pain of this nature begins to rear its ugly head even a tiny bit, we have to be extra vigilant at maintaining GREAT core strength and integrity. Dr. Goodman’s Foundation Exercises are super awesome for those of us with this problem but another fantastic - secret trick is kick-board work. Get in the pool (especially in off season but also 1-2x/week in season) and do laps with a kick board. Keep your legs mostly straight and kick from the hip and low back. I do 3 laps increasingly harder and the 4th lap is an easy frog kick. Recover and repeat. I’ll to 600-800 yds of kicking. After just 2 or 3 pool sessions, my back feels awesome!