Regular Expression for language
Note that your grammar is regular. Quoting from wikipedia:

A grammar is regular when no rule has more than one nonterminal in its right-hand side, and each of these nonterminals is at the same end of the right-hand side.
Every regular grammar corresponds directly to a nondeterministic finite automaton, so we know that this is a regular language.

In theory, every regular grammar generates a regular language. Also, its not hard to construct the relevant NFA for the generated language: for a specific example on how to do that, you can click here (this is actually what has been done in @Matthieu Latapy's answer). Once you have an NFA for the language, you can translate it into a regular expression (there are several ways to achieve this based on state removal methods which are a bit tedious: see here).
BTW, you already know that your language is all words with &quot;odd length and odd number of b's&quot;. It is easy to build a DFA for it consisting of 4 states (hint: your language is an intersection of two languages, each having a DFA with two states).