First, the promising apprentice must display some « interesting or promising » abilities. When can the Bonisagus gage that? Either the master is proudly flaunting the abilities of his pupil – ill-advised since he must be aware of the risk of having his pupil taken away, or a sodales of the master is advertising said abilities. But he is also aware of this risk, so either he does it on purpose or let it slip accidentally. Then the news must reach a Bonisagus looking for a pupil.
So, unless the mage is in Theban Tribunal where apprentices are « auctioned », there is the aspect of being aware of a promising student. Unless he has a Supernatural ability that is well-developed, it is unlikely that a mage will be able to gage that his pupil is gifted until several years within apprenticeship when he will be involving his apprentice in « real labwork ». One can only notice Inventive genius while working on new spells or enchantment, focus can only be spotted when the apprentice is learning or casting relevant spell, etc… There might be some signs or tells that a mage with experience can decipher, but IMHO, there is quite some room for misinterpretation, so an "interesting" virtue will only be discovered at least a few years after training begun..
Which can lead to some interesting stories in itself: what if a mage was trying to trick a Bonisagus into snatching an apprentice that is not so brilliant?
What if a Bonisagus wants to frustrate mage by stealing his apprentice? He would have to walk a fine line between depriving him of power and « honest » Boni-snatching – see HoH:TL for what is acceptable practice.
High intelligence (+3 or above) is likely the attribute that can be spotted the most easily: the student should be able to grasp quickly concept and learn faster – but bear in mind that there is nothing in the rule that translate well to show his superiority.
Mechanically, if I had to design a truly gifted apprentice, he would be one that has some virtues without counterbalancing flaws, or more than 10 points of virtues, with most virtues being hermetic, supernatural or boosting relevant attributes, and flaws being rather mundane, not hampering significantly his magical abilities.
Based on that, one can assume that in most case, the apprentice is already several years into his apprenticeship: he knows latin, basic magic theory, Artes Liberales (so he can read/write), his Arts are opened, possibly knows already a few simple spells.
That’s as many years shaven off that the Bonisagus does not need to cover again.
Apprentice, until they are Gauntleted, have no legal rights. They are a property of their master. That’s a cold-blooded fact. So no, an apprentice cannot avoid being sworn, because he is not yet a full-fledged mage, so he does not have a say. He can botch his Gauntlet by failing his magic theory exam, to further embarrass his master, but what would it be good to him? His master could literally kill him in front of his peers and legally nothing would happen. It is a Very Bad Idea, he can wait a few minutes after being Gauntleted to embarass his master.
However, as soon as Gauntleted he can renounce his House, it would be a huge slap in the face of his master. However, since he is a mage, he can be targeted immediately by a Wizard’s war by his own pater – but at least, he cannot be slayed immediately (slight improvement from the previous case). Before doing so, the apprentice must have thought carefully of his next move, and must have look for allies to protect him, a covenant that could offer him protection, Aegis and ideally another House that would be willing to accept him (although he has a year to do so – this is no secret, so any apprentice that is considering renouncing his House should be aware of that after just a tiny bit of research).
Regarding loyalty, it is really a matter of pater-filius relationship. What was the relation with the initial master? How was he treated by the new master? If the initial master had a strong relationship with his apprentice, was he allowed to visit him, give him advice, or exceptionally taught a few seasons on a topic the Bonisagus master was not well-versed (a supernatural ability for example) – that could account for Good Parens virtue and Mentor flaw.
There is - usually - no powerful Mentem spells used to enforce/erase loyalty. In fact, day-to-day brainwashing – if it is the goal – is a lot more efficient, especially considering that we are talking about kid/teenager raised in a peculiar environment – no real parents, no usual family, little to no friends of their age due to the gift effect…
[Edit: Levant replaced by Theban]