Question: I don't know why, during Diwali, the Bengalis celebrate Kali Puja? Why don't they worship Goddess Lakshmi and Ganesha?

Answer: 
Not only Bengali Hindus, but Axomiya, Oriya & Maithil Hindus also do the same, following the Tāntrika injunctions.

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> कार्तिके कृष्णपक्षे तु पञ्चदश्यां महानिशि । आविर्भूता महाकाली योगिनीकोटिभिः सह ।। अतोऽत्र पूजनीया सा तस्मिन्नहनि मानवैः । बलिपूजादिकं सर्वं निशायां क्रियते तु यत् । तत्तदक्षयतां याति कालीविद्या प्रसीदति ।।
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> *Mahākālī* manifested on the *mahāniśi* of the 15th day of the dark fortnight (i.e new-moon day) in the month of *Kārtika* accompanied by a crore of *yoginī*s. So She is worshipped on that day by humans. All activities like offering animal sacrifices & conducting worship done in that night yields unperishable merit & satisfaction to *Kālī*. [*Viśvasāra Tantra*]
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> तुलार्के बहुले पक्षे पञ्चदश्यां महेश्वरीं । यथोपचारैः संपूज्य महानिशि नृपो भवेत् ।। शनिभौमदिने चेत्स्यात् ततः शतगुणं फलं । तत्रोभयदिने भूतयुक्तकुह्वां महानिशि । इमां यात्रां कारयित्वा चक्रवर्ती भवेन्नृपः ।।
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> One becomes a king by worshipping *Maheśvarī* on the *mahāniśi* of the 15th day of the dark fortnight when the Sun is in conjunction with Libra (i.e the month of *Kārtika*) with the pre-required articles. The merit acquired is a hundred times more if the day falls on a Saturday or Tuesday. If this festival is observed on both of those days (of the week) with the *mahāniśi* occuring at the conjunction of *bhūta-caturdaśī* with *amāvasyā*, then the performer becomes an emperor. [*Kālīkalpa Tantra*]
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> **History Of Kali Puja**
> 
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> The pujas in Hinduism are not based on the Vedas. They are based on
> individual traditions. Bal Gangadhar Tilak started the Ganapati
> festival in Maharashtra to foster nationalism and it has been a custom
> ever since. In a similar way, Raja Krishnachandra who was the king of
> Navadipa started this Bengali puja of Mahakali in the 18th century.
> The tradition was carried forward by his descendants and the other
> wealthy zamindar families in Bengal.
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> As this puja was basically under the patronage of the rich and famous,
> it survived on a grand scale. Today, Kali puja is second in grandeur
> only to Durga puja in Bengal.
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> 
> **The Myth Of Mahakali**
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> 
> There is always mythical story to explain our rituals or pujas. So it
> is for kali puja. Once upon a time, two asuras, Sumbho and Nishumbho
> plagued the Earth and the Heaven. Thus the gods prayed to Goddess
> Durga who is the eternal Shakti of the Universe. To answer their
> prayers, Kali was born from the forehead of Durga.
> 
> 
> Kali attached the errant asuras with a 'khara' which is kind of
> twisted sword in her hand. Once she started slaying the asuras, her
> thirst for blood was aroused. She made a garland of the heads of dead
> asuras and wore around her neck. Then she started slaying anyone who
> came in her way. To soothe her anger, Shiva (who is her husband) lay
> in her path. When she stepped on her husband in her fury, she stuck
> her tongue out in regret. Her fury ended at than moment and that is
> why she is portrayed with her tongue stuck out and her foot on Shiva.
> 
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[Source](http://www.boldsky.com/yoga-spirituality/faith-mysticism/2012/kali-puja-diwali-031457.html)