In Aliens, it appears that Bishop awakes from being frozen. But why should he have been frozen in the first place? I can understand Ash being frozen, this was necessary to allay fears that he was actually an android. There was no need for such subterfuge in Aliens, since it is readily understood (with no issues) that Bishop was an android (until Ripley found out).
The film's official novelisation confirms that Bishop certainly doesn't need hypersleep. As the journey nears its end, he's already interfaced with the ship's computer and is helping to bring the ship back to ready status. This includes making sure that the crew is waking properly and popping open their (and his) pods.
Fourteen dreamers this trip. Eleven engaged in related morphean fantasies, simple and straightforward as the vessel that carried them through the void. Two others more individualistic. A last sleeping under sedation necessary to mute the effects of recurring nightmares. Fourteen dreamers-and one for whom sleep was a superfluous abstraction.
Executive Officer Bishop checked readouts and adjusted controls. The long wait was ended. An alarm sounded throughout the length of the massive military transport. Long dormant machinery, powered down to conserve energy, came back to life. So did long dormant humans as their hypersleep capsules were charged and popped open. Satisfied that his charges had survived their long hibernation, Bishop set about the business of placing Sulaco in a low geo-stationary orbit around the colony world of Acheron.
Which brings us to the question of why he isn't just up and about before the crew awaken. This likely comes down to the need for him to appear human in order to mesh well with his comrades. The Colonial Marines Technical Manual shows that if he looks (or presumably acts) in an inhuman way, his fellow soldiers won't bond with him. Joining them in the freezers is a small price to pay to look like 'one of the guys'.
Although a synthetic's cosmetic appearance would seem to be a superfluous feature, especially in a military model, practical experience has shown that it is a necessary component to maintaining combat unit efficiency and integrity. Most human soldiers are psychologically unable to interrelate with an inhuman-looking android; as a result, the physical appearance and simulated behaviour patterns of synthetic units are designed to particular specifications. Most synthetics in Colonial Marine service appear as mature, average males or females around 40 years of age. Their personalities, idiosyncrasies aside, can best be described as passive or non-threatening. Some studies published in recent years have suggested that androids have an important role to play within small infantry units, both as an impassive neutral party, and as a maternal/paternal influence in nurturing and sustaining the group dynamic at optimum efficiency.
There are no definitive sources about how the stasis process works in the Alien franchise, but it appears to be used for several reasons. First, it allows the crew to "skip over" the extremely long travel times necessary for interplanetary transport. Second, it provides a measure of protection from the deleterious physical effects of extended space travel. Third, the ship can conserve power by removing the need to heat and oxygenate large areas to make them habitable. While an android like Bishop would have no need for life support systems and would presumably not get bored on the long journey, it does seem likely that his systems would require maintenance and upkeep if kept running for extended periods of time, and he might also suffer ill effects from the ship's acceleration, exposure to cosmic rays, or other phenomena. Since the ship's automated systems were capable of monitoring the crew and waking them in the event of an emergency, having an android (whose primary function is as a science officer) active as well seems like a waste of resources.