A radical Islamic group's death-threat to Indian cricketers may have forced the hosts to provide stifling security to the visitors who arrived Wednesday, but the Indian duo will not lack enthusiasm when they step on the field for the opening Test of a two-match series on Friday.
Tendulkar is just one three-figure knock short of equalling compatriot Sunil Gavaskar's world record of 34 Test centuries, while leg-spinner Kumble needs one victim to overtake Kapil Dev's Indian mark of 434 Test wickets.
"It's an honour to play in a Test series where Kumble and Tendulkar will achieve their milestones," said India captain Sourav Ganguly.
"It's been a great experience playing with them and I'm keen to see them reach the records at the earliest."
Kumble and Tendulkar must be licking their lips in anticipation of playing Bangladesh, who have been struggling to compete with international sides on an equal footing since gaining Test status in 2000.
Bangladesh have lost 29 of their 32 Tests, sparking a debate whether they gained the Test status prematurely. The remaining three matches -- two against Zimbabwe and one against the West Indies -- were drawn.
India, who recently climbed to the third position in the International Cricket Council ratings behind only Australia and England, start as strong favourites.
The series will also provide the Indians with an opportunity to improve their batting and bowling averages after below-par performances in the recent home Test matches against Australia and South Africa.
If any Indian sorely needs a big score, it is Tendulkar who has suffered a lean patch since returning to international cricket in October after an elbow injury.
The master batsman, the fifth-highest scorer in Test cricket with 9,595 runs, has seven single-digit scores against his name in the last 10 Test innings.
Tendulkar may have struggled against Australia and South Africa, but is expected to return to his big-scoring ways against Bangladesh whose bowling attack has rarely posed a major threat to big teams.
Kumble has just to complete a formality, considering his awesome form. He grabbed 76 wickets in his last 12 Tests, giving a fitting reply to critics who had begun doubting the leg-spinner's credentials.
He is now behind only Australian leg-spinner Shane Warne (552), Sri Lankan off-spinner Muttiah Muralitharan (532), retired West Indies paceman Courtney Walsh (519) and Australian fast bowler Glenn McGrath (463).
Kumble is set to extend his successful run on low and slow Bangladeshi pitches which should favour spinners. He is capable of posing a major threat to the hosts while bowling in tandem with off-spinner Harbhajan Singh.
Bangladesh have had a few moments to cherish since making their Test debut. They exceeded expectations in their very first innings, compiling 400 against India.
They came close to posting a maiden Test victory last year before losing to Pakistan by one wicket at Multan. Their best this year came in the West Indies when they earned a creditable draw.
Bangladesh will be seeking inspiration from these performances to put in an impressive show against the formidable Indian tourists.