Not sure I am confusing it. The new breakdown is:
BBKA £17 (£2 rise)
Dorset BKA will be £6 (£1 rise)
Therefore £17 + £6 = £23 + £4 (Association Fund) = £27.
The Committee suggests our subscriptions be increased to £28 being a £1 increase in the Association Fund.
That's probably typical. There are three tiers to pay subventions to, BBKA, County (Dorset) and local. The BBKA is a uniform capitation nationally, the county/local split depends largely on structure, a federation of independent associations (like Middlesex) has a relatively small county subvention but larger local sum. And also typically, the "annual membership" includes two different insurance payments but they are not separated out in the proposed "annual membership" set at 28 pounds on the application form. It's not separate because you don't have an individual opt in or out, only collectively as an association.
The 3rd party and product liability insurance is included in the BBKA sub. I don't have any old BBKA accounts to hand but as I recall the 3rd party insurance premium was in the teens of thousands for 20 thousand or so members. If you left BBKA, you might want to replace that with a separate policy. The starting point is somebody like NFU mutual as used by Bedford, Daredirect as used by biobees, Towergate or some other broker. Chances are it's a little more expensive per head because of the overheads for a smaller group but not excessively more.
The BDI insurance (I'm guessing) is subscribed to at county level. So 2 pounds of your 6 will go to BDI for disease insurance. Many associations don't separate it out because it's subscribed to on an association wide basis although the premium is capitation based. Some county associations (I heard including Yorks for example) leave it to the local associations to decide. That is, at whatever association level it's two quid for every full member whether they have bees or not. If they have more than three hives the premiums increase to the individual. The "gotcha" is that if you take in a swarm or split to over the declared number you invalidate not only your BDI insurance but anyone else's who shares an apiary with your colonies, such as an association apiary. In practice I suspect most beekeepers think they are covered by BDI on shared apiaries, when they are probably not.
There is nothing to stop an independent association subscribing to BDI, just like Furness do. There's also nothing to stop any BBKA affiliated association not subscribing to BDI as several either don't or plan to drop it next year. But that is an association decision, not individual.
There are also associations who have made the collective decision to subscribe to other publications and bodies. some include a Beecraft subscription in the annual membership. Some may get Beekeepers Quarterly or Bees for Development, but I don't know any offhand. When the round of increases starts to pile up, it's time to start considering the options and what the membership think is good value and worth paying for. I think it's only fair that the position is made clear so that members can collectively decide.