It is important to press the bushes in on the outer sleeve only. Otherwise the inner sleeves can stop the outers from fully bottoming
As I understand it the outer sleeves don't 'bottom out' on anything. When you press them in they should be flush with the outside of the swinging arm and this can be achieved by pressing them in with a hydraulic press, or by the method that Dave described. The important thing is that you use something that allows the outer sleeve to end up flush with the end of the swinging arm and does not allow it to travel any farther than this. The bore of the swinging arm is reduced in the middle of it, which means there is a 'step' there that stops you being able to press a bush all the way through the swinging arm. You have to take them out either left or right. This reduced section /step in the bore is not very long and if you pressed the bushes in with, for example, a jig with a slightly smaller outside diameter than the outer sleeves of the bush, you could end up with them a long way into the bore of the swinging arm before they 'bottomed out on this 'step' inside the bore of the swinging arm. Which wouldn't be good.
The other issue is the inner sleeves, which (once again as I understand) should butt up to each other in the middle of the swinging arm. This means that when you fit the swinging arm, spindle and nut and tighten it up, the inner sleeves are trapped in between the main frame side cheeks. Any up and down movement of the swinging arm will then flex the rubber in the bushes around the swinging arm spindle axis. The rotary movement of the swinging arm at this point is very small.
I have had a problem with bushes in the past where the inner sleeve dimensions have not been correct. If this dimension is more than it should be (they are too long) they are forced outwards, once the outer sleeve is all the way home and flush with the swinging arm. This will make the whole distance across them too large and they will not fit in between the main frame side cheeks, as well as stressing the rubber in the wrong 'axial' direction.
If the dimension of the inner sleeves is too short then you have the problem of them not being held tight enough between the main frame side cheeks because they are not butted up against each other. This means that you have the possibility of the swinging arm and bushes rotating on the spindle, which will wear it out eventually.
After doing a couple of silentbloc bush replacements, I have come to learn that it is a pretty straightforward job (if you have the right tools) but it is very important to check and verify the dimensions of the bushes in the frame before you attempt to press them into the swinging arm.
This is how I believe things should be, after researching the subject using documentation, advice from others, actually doing the job for real and making mistakes in doing so, which I have learnt from (the hard way).
I have made up a few tools and jigs in order to carry out the job of getting the swinging arm out of the bike (the swinging arm spindle on my bike was a nightmare to remove the first time I did it) and to press new silentbloc bushes into it. I found the easiest and cleanest way to get old silentbloc bushes out is to chain drill through the rubber and then use a big taper tap to rip the inners out. I have heard that if you use a big enough drill bit you can break through the outer sleeve with it and then the whole bush will come out using the same method. I am lucky enough to have access to a machine shop, so once I had got the inners out I put the swinging arm in a milling machine and ran an end mill down the outer sleeve until it 'sprang' loose and it literally fell out.
If anyone wants any details of the tools and jigs I have made I would be happy to pass them on.
The parts that I made for getting the swinging arm spindle out, utilising a very heavy sliding hammer, will be very useful to anyone who experiences a spindle as stubborn as mine was to remove.