Any room containing a bath or shower is a bathroom. OK seems a bit simple but once you fit a bath in a bed room it has to follow bathroom rules. Before 2008 there were special rules for bedrooms. But in 2008 the rule about sockets in a bathroom was changed, they are now permitted if over 3 meters from bath or shower. In real terms bathrooms are not that big and it is really to allow a socket in a bedroom containing bath or shower.
The three zones 0, 1, and 2 will also apply and it says what may be fitted and where. Already covered 3 meters rule.
As to earthing not an easy answer. With existing it depends on RCD protection. With new RCD protection is required on all items in a bathroom including the lights. Because of this the bonding rules are relaxed.
What I am not certain about is if a bath is added what version of BS7671 must be applied. I may be the one in force when wiring was done. Or more likely it is current one.
Under 701.512.3 it with a lot more states:- Except for SELV socket-outlets complying with Section 414 and shaver supply units complying with BS EN 61558-2-5, socket-outlets are prohibited within a distance of 3 m horizontally from the boundary of zone 1.
There are two pages of regulations just on bathrooms. Clearly can't post it all. Personally if feed with plastic pipes I would not bond. However if metal pipes are used I would bond. Assuming it is RCD protected.
It say:- Where the location containing a bath or shower is in a building with a protective equipotential bonding system in accordance with Regulation 422.214.171.124, supplementary equipotential bonding may be omitted where all of the following conditions are met: (i) All final circuits of the location comply with the requirements for automatic disconnection according to Regulation 411.3.2 (ii) All final circuits of the location have additional protection by means of an RCD in accordance with Regulation 701.411.3.3 (iii) All extraneous-conductive-parts of the location are effectively connected to the protective equipotential bonding according to Regulation 4126.96.36.199.
701.411.3.3 Additional protection by RCDs Additional protection shall be provided for all circuits of the location, by the use of one or more RCDs having the characteristics specified in Regulation 415.1.1. NOTE: See also Regulations 314.1(iv) and 531.2.4 concerning the avoidance of unwanted tripping.
Also remember that a room with a bath or shower is a special location and as such the LABC needs informing of any electrical work done in the areas under the Part P law. Again I am not clear as to with either kitchen or bathroom what happens if it was not a kitchen or bathroom when the work was done.
If we take a typical kitchen refit first job is rip out work surfaces which means it's no longer a kitchen, then do all the electric work, then plaster, then fit new kitchen. Clearly although no work surfaces (food preparation areas) which mean it's not a kitchen it is unlikely any court of law will look at it that way. The same I would guess will apply to you. Although work may have been done while only a bedroom any work done to prepare for a bath likely the court will deem should be notified.
However the problem will likely only arise when either you try to sell house or some accident happens. But I am sure you will agree we would like to avoid an accident and as a result I would consider not DIY'ing even if you could wangle your way around the law.