GI motility is a fairly complicated area and can have a wide variety of causing delay. You really need to get a Gastric Emptying Study done to determine if it could be because of gastroparesis and an Endoscopy exam to see if there is just a stomach related cause.
It can take a lot of investigations, and sometimes years, to get to the bottom of things as it can be the result of things such as enterovirus, autoimmune antibody related, muscle or nerve signalling dysfunction, gut bacterial imbalance, connective tissue disorders, impaired blood flow to the bowel, autonomic neuropathy etc etc etc
Is it only liquids that present a problem or foods too? There was a small Australian study into motility dysfunction in CFS that found liquids were delayed but solids emptied at a normal rate.
A quick test your G.P. can do that can indicate if the problem is one of impaired blood flow to the bowel (which may be more prevalent than alluded to in the medical literature because it rarely gets tested for) is to listen to your bowel sounds for an epigastric bruit. If you have one of these, it's likely that eating and/or drinking will result in abdominal pain too about half an hour later.