TL;DR: By charging them under non-political charges (whether fabricated or real), of course. However, it is not clear to me that they would actually do so.
Not playing devil's advocate here, but I would like to point out some finer details that people have not yet mentioned.
The concern that politically motivated extradition may happen under the proposed bill is certainly valid. Many political dissidents in China were arrested under non-political offenses: artist Ai Weiwei under economic crimes, lawyer Zhao Lianhai under the crime of "picking quarrels and provoking trouble" (寻衅滋事), etc. These are perfectly valid concerns, and not only w/ regards to China! In the case of Julian Assange, for example, many have believed that the Swedish sexual assault investigations against Assange were conducted at least in part to get him sent over to the U.S.
Of course, comparing to the (according to many) already notorious U.S. criminal justice system, the Chinese judicial system has an even worse reputation (and for a good reason) for not following accepted criminal investigation standards in many cases, both political and apolitical, making the aforementioned concerns even more valid.
However, it seems to me that this is mostly a theoretical possibility. For most Chinese dissidents, the way to get them arrested would not be legally arresting them and sending them to the police or a People's Procuratorate Office. In the 2015 Hong Kong bookstore disappearances, those who disappeared were never arrested at all! In fact, very few political dissidents were legally arrested.
Therefore, it is very unclear that the extradition bill would be used extensively in a political fashion: the Chinese government have been mainly using extra-judicial measures to capture and arrest dissidents anyways, and regardless of whether an extradition bill exists, they would just continue to do what they have done it. If they can do it without going through a long extradition procedure, why would they have the motivation to go through it? (Think: how many Guantanamo detainees were actually presented with an arrest warrant and given a Miranda wraning, or captured in battle and informed of their rights under the Geneva Conventions?)
In conclusion, while there is a real possibility that the bill might be used to extradite people under political intentions, the fears that the extradition bill would be used extensively for political purposes and is mainly politically intentioned are mostly unfounded. Surely, in theory that there are plenty of ways that people can be extradited to mainlanc China if the bill comes into force, but in case real political "extradition" happens, it is likely to be extra-judicial, rendering discussion about the aforementioned theoretical possibilities moot.