Explanation:

- Savitha Sastry: She is a renowned contemporary Bharatanatyam dancer, but she has not received Padma Shri (1981) or Padma Bhushan (2003).

- Mallika Sarabhai: Famous dancer and activist. She is known in both Bharatanatyam and Kuchipudi, but didn't receive the Padma Shri in 1981 or Padma Bhushan in 2003.

- Rukmini Devi: A legendary figure in Bharatanatyam revival. She received the Padma Bhushan in 1956 and Padma Vibhushan in 1956, not the years mentioned in the question.

- Padma Subrahmanyam: She is an acclaimed Bharatanatyam dancer, who received the Padma Shri in 1981 and the Padma Bhushan in 2003.