Well... I am going to try and put some logic and solve the unsolvable.
First off, the real (as in "real life") reason to why the egg got on that ship is bad script writing combined with lust for money to make an unnacessary sequel.
Now, the following is PURELY fan fiction (since I have not read the novelization nor comics).
a) Burke knew coordinates of the derelict, meaning he knew exactly where the eggs were (which is clearly shown when Ripley occuses him of sending colonists to find it).
How much time passes between that marines arrive to the colony and Hudson finding colonists? Or put it this way, how much time passes between Ripley finds Newt and Hudson locates colonists on the map? Simple as it is: we do not know. It may have been an hour, but for all that is shown in the movie, it could be 48 hours (that is a bit overexaggerated, but you get my point). The flight time that Bishop mentions from Sulaco to the colony is approximately 35 minutes (I do not know if that is exact because I do not remember all his lines in the film out of the top of my head).
Meaning, that Burke would need about an hour and a half to go to the derelict, pick up eggs, fly the first dropship (remember now, it is not destroyed yet!), get back and return to Operations as if nothing had happen. We continue with this hypothesis and try to clear out the blanks to make it a plausible theory.
b) Burke could most likely not do all those things himself, he would most probably need help. But who says that for example if he would come to Spunkmeyer and Drake and sad "Hey guys, wanna earn couple of billion dollars? It is easy, we go to this place, we pick up an egg, transport it to Sulaco, leave it there unnoticed. When we get back to Earth we will share the money, just us 3. And the best part of all, no one gets hurt.", who says that they would react in the same way as Ripley did and turn him down. I would most likely think a couple of guys like them would answer "Sure, why not." Especially since they do not know what threat xenomorphs possess due to the fact that they have not even encountered them yet.
So they all go to the derelict, they manage to pick up one or a couple of eggs (depending on wether you believe in "twin" theory of one egg been able to hold two facehuggers) and lets just think they are skilled enough to prevent accidents and do not awake any other eggs. They put it/them in a bag (or whatever) and they tie it up very hard so that even if the egg(s) open the facehugger(s) wont be able to get out of the bag. They then transport this cargo to Sulaco, safely, no rush (as Hudson is still looking for survivors in Operations).
c) When they are on the ship Burke says to the others to wait on the dropship while he transports the eggs and hides it somewhere on the ship. For some reason he chooses to attach it/them to a wall somewhere near cryotubes in a 45 degree angle and somehow succeeds doing so. At this point the egg is still in a bag so that even if a facehugger gets out it possesses no threat. But the minute Burke gets out the surface of the egg somehow "eats" through the part of the egg between the wall and the egg itself, perhaps by realising a weak acid that also works as glue. The bag then slips off of the egg while the egg remains on the wall (due to the glue effect of the acid). He then returns to the dropship that flies them back to the colony. He reprograms Sulaco to not show any signs of the egg been omboard, hence why ripley did not knew about it in the end.
After encountering xenomorphs marines understand what dangerous species these are and would no longer support the transport of an alien egg back to Earth even for the money. The only problem is that the marines that knew of an alien been omboard the Sulaco die during the first battle. So only Burke knows...
d) After understanding the physiology of xenomorphs Burke realizes that it would save a whole lot to not need to find a body for the facehugger to jump on back on Earth. So he decides to try and make Ripley and Newt impregnated. He fails, miserably...
...
This is pretty much the only true logical explanation I can see that does not contradict movie in any direct way. I know this assumption is not flawless and needs improvement, but it makes some sense to me.
