Yes, three days are sufficient to explore.
Day 1: sight-seeing: Wat Arun, Wat Pho, Grand Palace, Chao Phraya river tour. Grand Palace can take time to explore but the rest of the places are not time-consuming.
Day 2: Shopping and sightseeing: Sukhumvit, Siam square, Asiatique night market and waterfront, Khao San Road in the night.
Day 3: For budget Shopping: Chatuchak market during (Sat-Sun), Pratunam (Sat-Sun) and MBK Center.
Note: Your schedule could be busy but if you are able to cover these places then you have seen most of Bangkok.
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