Firstly, good on you for recognising you need to start getting proper medical help for your bladder issue. It is always so difficult to face medical stuff and it is those initial, tentative steps that feel the hardest. It seems to me, from what you have said, that there are two issues here. You need to explain to your doctor that you have been having issues with your bladder for some time and you are apprehensive about whether to wear a diaper to the appointment. The second is that you have always dreamed of being incontinent and now it is possibly happening you feel a little lost. If I have missed anything please let me know.
If you have been wearing protection to deal with the dripping then changing your routine to save a little embarrassment may not make much difference to your overall situation. It would appear that you need to explain to the doctor how you have been managing your condition so far. What use would it be to leave out the diapers to save face when you are going to be talking about wetting issues in the first place. I totally understand how it would cause embarrassment and the conversation will be difficult but lying to a health care professional could lead to them diagnosing incorrectly and prescribing the incorrect treatment.
Thinking on this further, worrying you may not get the correct treatment may be a bit of a stretch when the only part you will be leaving out is the practicalities of using a diaper to contain the actual issue. As long as you speak openly about the dribbling you should be fine. It comes down to how comfortable you feel in the discussion and what information the doctor actually needs. It may be perfectly fine to leave out the diaper part if you feel it will be too much to deal with. What is important is that you seek the doctors help and get on a path to recovery as not seeking help for problems like this can lead to worse things in the future.
This brings us onto the next point concerning your fantasies of being incontinent. Reading many of the communities stories here I have not seen any that include any enjoyment of being incontinent. There are plenty who have explained they have learned to accept it and possibly enjoy the diaper side of it but I will look to others with more experience to give their thoughts on this aspect of incontinence. My overall opinion, and it is just that, is that your pursuit of incontinence could lead to serious harm to not only your physical health, but your life in general. It would be better to seek a remedy for the dribbling before it gets worse.