Step 1: Recall behavior of phenolphthalein.
Phenolphthalein turns pink in basic solutions (pH>8.3). If the solution remains colorless, it means OH$^-$ ions are absent.
Step 2: Recall behavior of methyl orange.
Methyl orange turns yellow in basic solutions (pH>4.4). Since the solution turns yellow, the sample must be basic in nature, but not strongly alkaline.
Step 3: Link with carbonate/bicarbonate ions.
If phenolphthalein gives no color (absence of OH$^-$), but methyl orange turns yellow (basicity present), then the alkalinity is due to CO$_3^{2-}$ or HCO$_3^-$.
Thus, OH$^-$ ions are absent, but carbonate/bicarbonate ions are present.
Final Answer:
\[
\boxed{\text{Presence of CO$_3^{2-}$ and/or HCO$_3^-$ but the absence of OH$^-$ ions in the sample.}}
\]