Not trivial at all. I have opposite problem, a reluctant bladder, and my GP has referred me to have it checked out.
Do you do pelvic floor exercises? If not, they may help, and even if they don't they are important for everyone :)
I learnt my method from gussiegrips on here, she's fab. 10, 10, 3. Pull up and hold for ten seconds (like trying to pull a tampon up inside you apparently), then ten quick squeezes (same movement but just pull up and then release), and then imagine it's a lift, pull up to the first floor, then to the second, and then to the third, then go back down to second, to first, and release.
When you pull up and let go you should feel a definite movement in the region. Another book (Tupler technique) described the pulling up as being like trying to pick up a penny with your lips. Anyway, do three sets of these each day, and if it is related to any weakness then it will probably improve :)
Pelvic floor weakness isn't just reserved for women with children, although it's more common.
Another reason may be a persistent UTI, so definitely worth seeing the GP. You could try some cystitis sachets to see if that helps.
I vaguely remember caffeine being mentioned as a trigger, so you could try avoiding that to see if it helps.
There's a long thread in the Exercise section about weeing whilst running. It was a while back now, but has some useful information, that's where I came across gussiegrips as whilst I have opposite problem, the causes can be similar!
Do you get an urge to wee and you can't hold it in, or does it happen when you cough, sneeze etc.? If it's the urge thing, try breathing out when you feel the urge, relax as much as you can. It's hard to make yourself do it, as you'll probably tense up and hold your breath, but holding your breath puts extra pressure on the pelvic floor. I was given the advice by my physio for pelvic floor related nerve pain, as I get spasms that I need to breathe through, but might be worth a try for you too.
I hope you can get an appointment ASAP and that this is easily sorted out 