Bureaucracy is a very powerful civic to improve the output of your Capital once your civ learns the Civil Service technology. Bureaucracy gives +50%

, +50%

in Capital but there are both limitations and additional benefits to understand to use it to best effect.
The first point to note is that the +50%

bonus is like most boni additive improving the output of all tiles and Engineer, Priest & Citizens specialists in the normal way and acts the same as having 2 forges in the city would (not that you can have 2 forges!).
The second point to note is that
commerce is increased by 50%. Certain manuals and official strategy guides incorrectly state +50% gold. This is because the initial release of the game used the commerce icon for commerce and gold which confused the authors. The Civilopedia is correct.
The third and most important the thing to note is that as commerce is multipled by 50% this increase is cumulative with the various building multipliers for

,

and

that are available from the likes of Libraries, Banks, Cathedrals etc, after allowing for the effects of the commerce slider. This is quite unusual and very powerful [I think the only other example of a cumulative bonus is the one associated with Financial Trait.] Other bonuses devalue the more of them you have for example if you have a Library +25% science bonus then your net University bonus is 40% not the gross 50% you might first think.
However as a direct result of the calculation, the +50%

multiplier does nothing for

,

and

received from specialists or for
gold or culture from buildings 
.
Therefore if you intend to run a Great Person (GP) farm focussed on Great Scientists, Artists or Merchants maybe based on the Caste System civic then it might be best not to have this in your Capital at least while you are running Bureaucracy.
Given a choice the Capital should use it's food surplus for a 'Cottage economy' rather than Caste System specialists.
Also there's no harm allowing religions to found outside the Capital as they will tend to do unless you do not settle your second city. Bureaucracy cannot assist their shrines which is actually quite a realistic seperation of Church and State. For similar reasons you don't need to worry about the location of the Spiral Minaret if you are fortunate to learn Divine Right in timely fashion.
Also if you are going for a cultural victory and have reached the Liberalism, adopt Free Speech and set culture slider to 100% stage you can be reassured that the gross boost to culture from the 100% bonus of Free Speech is
greater than 2x the boost you were getting from Bureaucracy (Free Speech works on the culture received from buildings as well as that from commerce). This applies even if there are no towns around your capital to benefit from the other effect of Free Speech.
However because the Free Speech bonus devalues with buildings bonuses from Cathedrals, Hermitage, Broadcast Tower etc, whilst the Bureaucracy one does not this may not be true if you have more than 100% culture bonuses from buildings combined with much more commerce based than buildings based culture. Specifically the break even point (ignoring towns and other cities) is when (2 x culture value of buildings) >= commerce * 100% * (buildings bonuses -100%)
Finally note that Priest specialists benefit from the +50%

bonus but not the +50%

one.