Tal Celes was another Bajoran in Starfleet, who explained that the Federation was "eager" to have Bajorans in Starfleet even though Bajor was not yet a Federation member.
Tal Celes served on Voyager. She was assigned to the ship before Voyager disappeared into the Delta Quadrant — at the time, Bajor was still not part of the Federation. From a conversation between Celes and Captain Janeway in the episode "Good Shepherd":
JANEWAY: We all make mistakes, even me.
CELES: Every day? Every time you report for duty? On Voyager it doesn't matter because nothing I do is that critical. Seven doesn't trust me with anything important. The crew is protected from my mistakes by the people around me, but out here I could get us killed.
JANEWAY: You went through Starfleet training courses.
CELES: I had to cram for every exam.
JANEWAY: At the Academy, I was infamous for my all-nighters.
CELES: Every night? Because that's what it took. That's the only way I made it through. Not to mention the sympathy votes. The conflict on Bajor worked in my favour. The Federation was so eager to have Bajorans in Starfleet that my instructors gave me the benefit of the doubt. So did you, when you accepted my application.
JANEWAY: You showed evidence of unconventional thinking. I liked that. Not everybody would have thought to retrieve that hull plating.
Essentially, Celes was encouraged to sign up for Starfleet for political reasons, even though Bajor was not yet a member world. However, Starfleet is a meritocracy and Janeway herself says that Celes showed evidence of "unconventional thinking", which worked in her favour.
Based on timing, Celes would have joined Starfleet just after Cardassia left Bajor and the Federation began sponsoring Bajor while Ro Laren would have joined while Bajor was still under occupation. However, we know that the Federation had been deeply concerned with the aftermath of its war with Cardassia and with the security of its borders with the Cardassian Union even before Cardassia's withdrawal from Bajor (for example, the events of TNG "Chain of Command"). It would not be out of character for both Starfleet and the Federation to welcome Bajorans who knew how to fight Cardassians and bolster support for an eventual Federation presence.
So one can conclude that:
- there were strategic and political advantages to having Ro Laren in Starfleet;
- Laren would have exhibited enough motivation and "unconventional thinking" to complete her training and be worthy of an official assignment.
Finally, from the official StarTrek.com database entry on Ro Laren:
As a sign of her inner strength and drive, Ro was able to overcome her tortuous childhood and won sponsorship as part of the stricter admission requirements of a non-Federation citizen to Starfleet Academy, graduating within the regular four-year curriculum with at least one class in botany that she later felt embarrassed by.