Are any investigations apart from what you mentioned have been done? Is there any over-weight or obesity issue?
I agree that it can be Helicobacter pylori issue and a triple therapy regime has to be taken for the full course to eliminate, these bacteria. But with a bitter taste occurring at night time it means the lower esophagus sphincter which normally closes, is not closing properly and let the acid content of the stomach come up to your mouth. This will need further investigations and a consideration of the hiatus hernia has to be done. Following can be done;
1) Barium upper gastrointestinal series
2) Esophageal manometry
3) 24 hours pH monitoring of esophagus
There are medication like reglan (metoclopromide) for enhancing esophageal and gastric motility. Taking them before the bed time helps in relieving the symptoms. This is a prescription medication and you have to get a prescription from your physician.
Please feel free, if you want to discuss it out further.
Yes, both of them can co-exist, so need some basic investigations to look for them.
Best wishes and kindest regards.