It depends on your definition of 'bus station'. Personally, I'd only include areas that are accessible to the general public, where you can get on or off buses. If you include areas that are sometimes referred to by a bus operator as a 'bus station' then, imo, the most central London one was at Waterloo, now the site of London General's garage that operates only the electric-bussed Red Arrow routes. It's in Cornwell Road, and in pre-TfL days was known at times as both Waterloo Bus Station and Waterloo Bus Stand for internal purposes by the generic London Transport. Planning and other restrictions would have hampered LT wanting to make it into a proper bus station, should LT have wished to do so: I must say I'm not aware that they ever wanted to.
The Kingsway tram subway that linked a smattering of North and South London routes featured an underground tram station for passengers. If the centre of Central London is Charing Cross, then that would have been the nearest if only visionaries had allowed it to continue and be converted to a bus station. Of course, far more visionary would have been to foresee the rebirth of the tram, but that would have been a stretch!!
Regarding Aldgate, I'd put the older-established London Bridge as being a tad more central, but that's nitpicking!