Oh, I'm not questioning the efficacy of bicarbonate - indeed, it will provide near instant relief the majority of the time.
The issue comes when the heartburn / reflux becomes constant, especially after eating a meal (even without normal "trigger" foods) - a lot of times, people are prescribed things like a proton pump inhibitor or other more powerful acid reducers. I'm not sure how many GP's are equipped to test stomach acidity; I would ask for a referral to a gastroenterologist to have that sort of thing checked out.
In my case, it was a combination of factors, stemming mostly from Eosinophilic Esophagitis and Esophageal Acid Reflux caused by premature relaxing of the lower Esophageal Sphincter. It caused my esophagus to become ribbed (like corrugated tubing) rather than smooth, which resulted in a host of problems.
The ironic solution for me was to increase my stomach acidity (so food didn't take quite as long to digest), combined with a mild PPI that has a secondary use in treating EE. It's so nice to be able to eat normally without fear of debilitating chest pains or food getting stuck!
Ultimately, it comes down to "if it works for you, it works" - after all, everybody is different