Before discussing Beatrix in-depth, it's important to discuss her home. Alexandria is a monarchy nation and is ruled by Queen Brahne at the beginning of Final Fantasy IX. It has a renowned and respected all-female army, the general of which is Beatrix. Her squad is also charged with guarding the Queen and her chambers. The city of Alexandria is also protected by the Knights of Pluto – a smaller, all-male group of knights led by Captain Adelbert Steiner. While Beatrix herself also has a respected (but feared) reputation, the Knights of Pluto don't command nearly the same level of respect – something that aggravates Steiner. Both he and Beatrix are incredibly loyal to their Queen and Princess, but they do have something of a rivalry going on at the beginning of the game. But more on that later.
While Queen Brahne was once known as a wise and benevolent ruler that seemed to be popular with her people, by the time Final Fantasy IX begins she has changed drastically. Since the death of her husband several years ago and the appearance of a mysterious arms dealer named Kuja, she has become cruel and greedy and is preparing Alexandria for war. Her daughter, Princess Garnet, has noticed the alarming changes and fears what it means for Alexandria and the neighbouring kingdoms. She does not trust the suspicious arms dealer, and clearly feels there is no one in Alexandria she can confide her worries in. Which, while later it is shown that both Steiner and Beatrix are incredibly devoted and close to Garnet, it's sadly understandable that she can't approach them. So, she decides to use the visit of Tantalus to her advantage – which works out quite nicely for the thieves. After all, it's much easier to kidnap a princess who wants to be kidnapped. Garnet's plan is to make her way to Lindblum and consult Regent Cid for help.
As it turns out, Garnet was right to be worried, and even more right to leave Alexandria when she did. While she does eventually make her way to Lindblum alongside Steiner and with the help of Zidane, her mother has begun an attack on Alexandria's other neighbouring kingdom of Burmecia, using her powerful army led by Beatrix to invade. Regent Cid in Lindblum has also been watching Alexandria and Queen Brahne's erratic behaviour closely, although does not take action against the events in Burmecia because he fears leaving Lindblum open for attack. While Garnet finds it painful to recognise her mother in this war mongering monster, she's also not letting her feelings excuse Brahne or pretend she's not responsible. This is in contrast to Steiner, who's only concern at this point is getting Garnet back to her mother in Alexandria because he genuinely believes this is a misunderstanding and the Queen is still good – even though she has sent violent Black Waltzes after them to retrieve Garnet. Beatrix, too, is at this point still loyal to the Queen - it takes her longer to realise she's been following the orders of a madwoman.