Hi Jez,
I run all of my LED's (wired in parallel) from a single 9v battery with a single resistor. It means you have a lot of wires running down the neck but I use tiny thin wire so it's OK.I get very good battery life using this method.
Putting LED's in a bass you are making yourself is very easy compared to retro-fitting as you can pre-rout all your channels and as you are only doing the side markers, even easier. You are bang-on with the fibre idea, although you could do yourself a massive favour buy buying some brass tubing from a model shop and making your actual dots from that. The fibre will fit right inside and can be held in place with epoxy or superglue. Cut the brass tubing to approx 4-5mm lengths and this will give you a nice tidy job, plus the brass adds a touch of class
When it comes to the fibre itself, bond it in place before you trim it back. Cut it with a scalpel and then polish it with 1200 grade wet or dry. The better finish you get on the end of the fibre, the brighter your LED will be.
Alternatively, as you are fitting the LED's before installing the fretboard, you could use a length of 2mm round acrylic (perspex). Bond this directly to the LED. You will get really good light transfer with this material and it's easier to work with than fibre. You still need to polish the ends though.
I'm guessing you are using 3mm LED's. These are fine for side-only dots but I would recommend using Surface Mount LED's for front markers it you ever wanted to install them. Before surface mount technology I had to modify each LED to make it fit and it was a major pain in the @$$. Status now use surface mount LED's in their basses, although they have a lot of problems with static when polishing.
Let me know if you need any more help
Scott.