The sense of never fully emptying is a symptom women rarely bring to a doctor, because it does not hurt and feels less alarming than leaking. Clinically it matters. Urine left sitting in the bladder is a medium for bacteria, and it is one reason bladder infections keep returning.
There are several common causes in women. The first is descent of the front vaginal wall, which lets the bladder pocket so that it cannot drain completely in one go. The second is a pelvic floor that is too tight, so the outlet does not relax during voiding. The third is behavioural: rushing and pushing to speed the stream up, which actually worsens emptying, and habitually holding on for hours so the bladder is repeatedly overstretched.
Things worth changing before your appointment: sit fully back with your feet supported, do not push and do not rush, wait twenty to thirty seconds and try again before standing up, avoid holding on well past the point you should have gone, and keep drinking normally, since restricting fluid to avoid the toilet concentrates urine and irritates the bladder further.
See a doctor if you have repeated urinary infections, a thin or stop-start stream, need to push to start, can feel a bulge at the vaginal opening, see blood in your urine, or cannot pass urine at all, which requires same-day attention. A pelvic examination combined with a urine test and a measurement of residual volume usually shows whether the cause is structural or muscular.