The story centers around Akaash, a young man from the slums of Bombay who dreams of becoming the next big star in Bollywood. Fate steps in when a rich pro-bono lawyer and his fiancée, an aspiring documentary filmmaker, arrive to prevent the demolition of Akaash's slum. Akaash quickly falls in love with the lawyer's fiancée, Priya, who happens to be the daughter of a famous Bollywood director, and the ticket to the top that Akaash needs. Complications arise as Akaash faces the reality of show business, fame, his love for Priya, and his obligations to his family, friends, and his Paradise slum.
The plot includes frequent reference to the change of name from Bombay to Mumbai of the titular city and references the identity issues that this raises.
The plot, format and characters of Bombay Dreams were revised several times. The book of the musical was rewritten and many songs were cut and other songs added to the show for the Broadway run.