There is no definite time period given for Homeless Bird and because the culture of India seems so backwards to us in the United States, it seems like it must have been set in the "long ago and far away" time period. This is not true. One can infer from the reading that the novel takes place in fairly modern times. The description of the cities, the fact that there are trains all point to fairly modern times.
The customs that to Americans seem part of the past are actually still part of India's present. Paying a dowry as part of a marriage arrangement is supposedly against the law in India, but the law is not followed, especially in rural areas. Girls are supposed to be entitled to education, but this also is not followed and many girls do not receive an education. Arranged marriages are still common, especially in rural areas, and very young girls are often married off to older men so that the girls' families can obtain money.
Read what the author herself says about the novel and why she came to write it at the link below.