Does washing soda (sodium carbonate) turn into baking soda (sodium bicarbonate) over time? I have some sodium carbonate. But it's over 20 years old and was not kept in tight bottle. I wonder if this compound absorbs $\ce{H2O}$ and $\ce{CO2}$ from air.

I guess I'd need to burn it a little to turn it back in case the answer was yes.
Industrially, sodium bicarbonate is produced by reacting sodium carbonate with water and carbon dioxide.  However, under normal household conditions sodium carbonate simply reacts with water or moisture in the air (it's hygroscopic) to form a hydrate - it doesn not form sodium bicarbonate. The water of hydration can be removed by mild heating (~100 C).  At high temperatures (>850 C) sodium carbonate can decompose according to the following equation.$$\ce{Na2CO3(s) -&gt; CO2(g) + Na2O(s)}$$