There is a prevailing belief that Draupadi took a vow to wash her hair with Dushasana's blood, and it is often stated that Bhima fulfilled this vow. However, it is important to note that the original Mahabharata by Ved Vyasa does not include any narration of Draupadi ever taking such a vow, nor does it depict Bhima going to Draupadi with Dushasana's blood to taint her hair. This particular narrative seems to originate from the famous play titled "Venisamhara." Venisamhara is essentially a heroic play, that draws its plot mainly from the Mahabharata, written by Bhatt Narayana who lived during Pallava period i.e. 275 CE to 897 CE.

In Venisamhara, Bhatt Narayana introduces the storyline where Draupadi is insulted by Bhanumati (character added by Bhatt Narayana as wife of Duryodhana), and Bhima subsequently vows to adorn Draupadi's hair with enemy's blood. It is essential to recognize that this specific narrative is a creative addition by the playwright and not present in the original Mahabharata text.

In Act 1 of drama Bhanumati asks, in an insulting tone, the question to Draupadi: O Yagnaseni (i.e. Draupadi), it is heard that five villages are being prayed for. Why is it then that your hair are not tied even now?
अयी याज्ञसेनी, पंचम् ग्रामाः प्राथ्यर्नत इति श्रुयते । तत कस्मादि दानीमापी ते कांशा न संयम्यते । (Page 42)

The original Mahabharata by Ved Vyasa does not contain any mention of Draupadi leaving her hair untied, indicates that Bhatt Narayana introduced this detail to intensify the dramatic confrontation with an element of vengeful anger.

Moreover, in the original Mahabharata, there is no record of Draupadi taking a vow to tie her hair only after washing it with the blood of Dushasana. Bhatt Narayana dramatizes this scene in Act 1 of Venisamhara by scripting Bhimsen's enraged response to Bhanumati's insult to Draupadi. Bhimsen vows to adorn Draupadi's hair with Duryodhana's coagulated and thick blood, expressing his determination to bring about this gruesome outcome using his powerful and relentless physical prowess. Exact shloka along with translation are as follows:
चश्चद्भुज़ श्रामितचण्डगदामिघात-
संच्राणतोरुयुगलस्य सुयोधनस्य
स्थानावनद्ध घनशोणित शोणपाणि-
रुत्तसयिष्याति कचांस्तव देवि भौमः ॥ २१ ॥
"Oh queen, Bhima will decorate your hair with his hands gory with the congealed coagulated, thick blood of Suryodhana (Duryodhana), with his pair of thighs well crushed under the strokes of the terrible mace brandished by his restless hands" (Page 44)

Apart from this, there is no mention in the original Mahabharata by Ved Vyasa of Bhima ever taking the blood of Dushasana to Draupadi. Towards the end of Chapter 62 of Book 8 (Karna Parva) of the Mahabharata, Bhima kills Dushasana:
8.61.16
दुःशासने यद रणे संश्रुतं मे; तद वै सर्वं कृतम अद्येह वीरौ
अद्यैव दास्याम्य अपरं दवितीयं; दुर्यॊधनं यज्ञपशुं विशस्या
शिरॊमृदित्वा च पदा दुरात्मनः; शान्तिं लप्स्ये कौरवाणां समक्षम
8.61.17
एतावद उक्त्वा वचनं परहृष्टॊ; ननाद अचॊच्चै रुधिरार्द्रगात्रः
ननर्त चैवातिबलॊ महात्मा; वृत्रं निहत्येव सहस्रनेत्रः
"When Dushasana fell in battle, my joy knew no bounds. Everything has been accomplished today, O valiant ones! Now, without delay, I shall present the second victim—Duryodhana, the sacrificial animal of the Yajna, to vultures, having severed his head. I shall also trample upon the wicked one with my foot, drenching my foot in the blood of the evildoer. Thus, I shall attain peace in the presence of the Kauravas."

Having spoken these words with immense delight, Bhima, his body covered in blood, roared loudly. The mighty soul danced exuberantly, as if he had already slain Vritra, the thousand-eyed demon.

The chapter concludes with this statement, and the subsequent chapter begins with the narration of the ten sons of Dhritarashtra attacking Bhima.

8.62.1
  दुःशासने तु निहते पुत्रास तव महारथाः
  महाक्रॊधविषा वीराः समरेष्व अपलायिनः
  दश राजन महावीर्यॊ भीमं पराच्छादयञ शरैः
8.62.2
कवची निषङ्गी पाशी दण्डधारॊ धनुर्धरः
अलॊलुपः शलः संधॊ वातवेगसुवर्चसौ
8.62.3
एते समेत्य सहिता भरातृव्यसनकर्शिताः
भीमसेनं महाबाहुं मार्गणैः समवारयन

[Sanjaya speaks]
"O King, when Dushasana fell, your mighty sons, heroes intoxicated with great rage, who never retreated from the battlefield, surrounded Bhima with their arrows, covering him like the clouds enveloping the moon.

Armed with armor, quiver, noose, and bow, Bhima, the wielder of the mace, the unshakable, and the holder of the bow, with his unfaltering and forceful prowess, was like the wind and the sun combined.

Approaching together, these brothers, afflicted by the calamity of Bhima, engaged the mighty-armed one, blocking his path with their arrows."

There is no mention in the original Mahabharata by Ved Vyasa of Bhima going to Draupadi with the blood of Dushasana and tainting her hair with it.