i had this same decision to make a couple of weeks ago.
A few months ago I bought a olympus c740UZ (whihc is a bridge camera) from fleabay.
Was ok, but I soon wanted something a little better, so i satrted looking around, determinded not to go down the out of budget dslr route.
I spotted a fuji s5600, and almost bought it but decided to do a little research.
Whilst doing so i headed in a high street shop (edited to apease the forum police) and to get a feel of one (highly recomended beofre buying any camera) and they had a s9600 on display.
I picked it up and it felt good, with a the zoom dial and manual focus dial actually being on the lens, which felt very good to me.
Came back onto this forum to ask the guys in the know what they thought of it, and to do some online reseach into the 9600
Then someboidy mention the Nikon d50 ki, refurbished for 264 (thats the same price as the best price I had found on the fuji 29600)
I searched and found the supplier and after going into a camera shop to have a feel of one (they only had a d40 though).. yup I ordered one, ready for my birthday (which was two days ago) and also got myself a sigma 70-300 lens and a very cheap (disapointed when it came because it was tiny, looked much bigger on the picture) bag.
Havent actually gone out with it yet (hopefully will tomorrow) but have played around with it in the house
Photograhy can be a massive finance drain but it can be very rewarding.
I would personally sugest, getting a cheap second hand bridge camera (i payed £50 for my olympus) and seeing :-
a) do you find yourself using all the manual options
b) are you quickly wishing you could do more with the camera
c) can you get creative with shutter speeds / aperatures / light sources etc
if yes to the above (specially a and b) save up a little and get an entry level dslr and lens
if the bridge camera is giving you good reuslts you are happy with or you find yourself just using Auto mode, then stick with that or get a higher end point and click compact.
for me, the decsion to leave my olympus and move up was largely due to some pictures I took at a Stoke City match, and Moon pictures, not quite giving me the settings I wanted.