You asked for a trick. Yes, there is a construction to add a single letter to the strings in the language of a grammar given in advance.
For simplicity I will start with a grammar in Chomsky Normalform, i.e., every rule is of the form $A\to BC$ or $A\to \sigma$, with $A,B,C$ variables and $\sigma$ terminal.
Assume there is a context-free grammar $G$ for a language $L$ then we can construct a grammar for "strings in $L$ with an extra $b$" in a generic way. We use the variables to hand down the instruction "add a $b$" to one of their successors. For each variable $A$ we introduce a copy $A_1$ that carries this task.
Thus, for every rule $A\to BC$ we add the new rules $A_1\to B_1C$ and $A_1\to BC_1$. Morever, we make it possible to add the extra $b$, with rules $A_1 \to bA$. Now starting with $S_1$ derivations are as before, except at some point in the derivation a single $b$ is introduced. Note that we need to generate a $b$ since variables $A_1$ cannot be rewritten into terminals. One tiny detail: the $b$ can only be introduced before a variable, so in order to append a $b$ we need the additional rule $S_1\to Sb$. (We need no other additional rules since a $b$ after a variable can be replaced by a $b$ before another variable, except at the end.)
