As far as I know it is a suite, including offices. There are probably a dozen or so that would nor have required the amount of money spent, that would have been suitable. I still find it hard to understand wht the taxpayer has spent £250,000 to £300,000 to save her a commute of an hour and a quarter (by car). Much faster by train of course!
Going by the information in Sarah, Duchess of York's book and also Charles's valet Stephen Barry's books describing the living quarters at Buckingham Palace, the royals there have rooms along a corridor. Andrew had a bedroom, sittingroom bathroom, Sarah moved in with him after they were engaged. (Diana was decoriously given her own bedroom, sitting room bathroom! She didn't share Charles's) Andrew's accomodation was not upgraded even after they had children, I gather nannies would have looked after the girls at the country house if the parents had city engagements and would sleep at BP. The offices are in a different part of the palace not with the living quarters.
Beatrice's apartment at St James's was formerly used by a royal courtier so it was a 'grace and favour' apartment, no rent was paid, a perk of the job. It hadn't been upgraded since the last occupant moved out several years ago, just like Clarence House was upgraded with new wiring and plumbing as well has bringing the building up to recent safety codes, so was this apartment. The government paid for the work to Clarence House as it's a public building, Charles paid for the interiors. St James's is a public building so the government has paid for certain parts of the renovations, (electrical and plumbing don't come cheap!) Being a historic building there would be quite a strict listing of what materials could be used. Andrew and the Queen paid for whatever was covered by the government. So I'm assuming it's for furnishings etc.
From the time of Princess Anne's 1974 kidnap attempt all HRHs have been given 24 hour police protection. (Before they didn't and minor royals got none) Police protection was again upgraded in 1979 after Earl Mountbatten's death. The royals needs to have 'secure' accomodation, in Anne's case, accomodation had to be created at Gatcombe for her police protection officers. Established royal buildings (St James, as Charles and his sons lived there for a time) are secure meaning that a police officer doesn't need to be stationed nearby, as in the next room for William when he was in student digs at St Andrews. Or a separate cottage on the same property as now with the house the princes share. I'm sure it was looked into as to where Beatrice could live, she was even photographed viewing some expensive apartments but security issues limited her choice. PPO would have to live nearby. (Whether or not she should have them is another debate, just as it's been pointed out the Princess Alexandra has 24 protection over her large estate where she lives alone, and is a very minor royal)
Currently all HRHs have 24hour protection having Beatrice living at St James's rather than elsewhere in London is more cost effective ( no nearby sleeping PPO) than if she lived in private accomodation.
As far as an hour commute being acceptable, it's not, I had this situation in a job I worked in. I moved rather than spend an hour each way commuting, I had better things to do with my time than spend it in a car for 2 hours a day! And that's on good days, knowing London traffic it wouldn't need much for the hours to mount, Beatrice was late her first day at the FO as she was caught up in a traffic accident. I remember William was too, on one of his job placements.