I bled my Elixir 5s at the weekend and I've got the process sorted so that it takes about 10 minutes per wheel. I just lent the syringes to a mate for him to do his and wrote him some instructions. I thought I'd paste them on here, too, in the hope that they help anyone who's struggled with this in the past.
Firstly, put in new pads if you're considering swapping them as it's best to get that done first. Next, with the wheel out, squeeze the brakes until, without squeezing the lever, the pads are just skimming the surface of the disc if the disc were in there - sounds daft but you have to overextend the pads on a lever squeeze to get them to return to a spot just the right distance apart. Put the wheel back in and check that it's not draggy - if it is, use a big, flat screwdriver to gently prise the pads apart a little. Put the wheel back in to start bleeding (if you haven't already) and get the front of the bike as high up as you can but so you can still turn the steering to vary the angle of the lever/master cylinder. A workstand is invaluable for this.
I fill one syringe full of brake fluid (put the lid on the brake fluid tin!!!!!) and snap shut the clip that squashes onto the pipe then, with the syringe pointing upwards, I carefully pull down the plunger a bit. Air comes out of solution and collects on the sides of the syringe and a bit of vigorous tapping of the syringe with a screwdriver will make the bubbles float upwards.
Try and get as much air out as you can then undo the clip and, with a rag round the brass screw end of the syringe and the pipe pointing skywards, push the plunger up to force out the air. Clip off the pipe. Remove the bleed screw from the caliper and attach the full syringe. The empty one attaches to the lever end.
Now it's time to start forcing new fluid into the system. Don't forget to unclip the clip on the syringe pipe before you start - it's messy if you forget! Steadily squeeze the lower syringe to push fluid through to the top syringe. As you're doing this, do the following:
1. Tap the caliper and brake lines with a screwdriver handle to get the bubbles moving upwards
2. Regularly flick the lever a little to let the air through the bleed hole in the master cylinder
3. Keep rotating the steering so that the lever is uppermost then the line to the syringe is vertical with the syringe uppermost. It lets more air out of the master cylinder.
At no point disconnect the syringes or pull fluid back into them. It means you have to start again.
Keep going until you've got just a centimetre of fluid in the lower syringe then use the clip to close the line on the lower syringe. Now close the clip on the upper syringe.
Next, with a rag wrapped around the master cylinder and the bleed hole pointing as upward as you can get it, quickly unscrew the syringe and screw in the bleed screw. Repeat with the caliper end (remembering the rag) and test your brakes for a fairly solid feeling.
Junk the fluid out of the upper syringe (it burns well so is good for starting fires/barbecues!), refill the lower (getting the air out using the clip-up-and-pull-plunger process) and start on the other brake.
I hope that helps.