Carcassonne builder and bazaars
tl:dr-  No, I don't think they should take another bonus tile.

Firstly I'm going to assume that by 'castle' you mean 'city'.  The castle in Bazzars refer to a specific token which the builder can not be placed on and your example seems to mean the player extended a city with a builder to.

I think a key word in the rules is 'immediately' in Traders and Builders.  Using the rules reference here it says as follows:- 


  If you place a Land tile that continues the road or city your builder occupies,
  you may immediately draw and place another Land tile. You place this tile
  following all the normal rules


then later it says :-


  You may place a meeple on both the first and second tile.


The rules for the Bazaars taken from here


  The placement of a bazaar triggers a bid for Land tiles.


Now in luie of anything better to go on I'm would do the rules saying 'immediately' before trigger.

The final semantic note to is that the Bazaar rules refer the whole process of auctioning and placing tiles as the 'Bazaar round'  it does not use the term 'turn'.  Turn is used in the Builder rules.  Both rules are very strict that no chain reactions can occur to trigger multiple auctions or builder actions in the same turn.

So my interpretation of your example would be as follows:- 
1) Player A starts turn and draws tile with bazaar and adds it to city/road they have with a builder.
2) Player A then optionally takes another tile and optionally adds meeples (or other pieces depending on expansion to those tiles.
3) The game is the interrupted for an Bazaar round.
4) Player A add that tile to extend city/road with builder.  However as they are not allowed chain reactions they do not get another tile this turn but may still optionally add a meeple/other token to tile just placed.
5) Player A's turn ends.