No, most Islamic scholars agree that playing bingo is haram, even if the stakes are small. The sin lies in competing on chance and luck, which constitutes gambling. Any game of chance is considered gambling, and gambling is prohibited in Islam. Even if no money is involved, participating in bingo is against the teachings of Islam.

And Allah knows best.

Sources:

• Pious Policies
• Tafseer Raheemi
• Ask Imam