Bis zu ihrem Abschluss in Psychologie möchte Andrea nicht umziehen.
Why ihrem after akkusative bis?
Bis is always an accusative preposition. Here the preposition that governs the case is zu (an always-dative preposition), that is why you have ihrem instead of ihren.
The preposition "bis" can be used with the german Akkusativ and Dativ as well. Usually "bis" with Akkusativ but if you use "bis zu" then the Dativ may follow (Temporal preposition).
Usually one can omit the "zu" when using "bis zu" and it seems "bis" would required always Dativ which is not true. You can find and construct a variety of sentences using either of the casi.
Best wishes, SG