“There are 73 state orphanages for approximately 9,500 orphan children. Three Baby Homes for Abandoned Children with the capacity for 250 babies. One Destitute Children's Rehabilitation Centre for 400 Children. One Vocational Training Centre for Orphans and Destitute Children for 100 children. Sixty-five Welfare and Rehabilitation Programmers for Children with Disability for about1400 children." > source

“There are also thousands of non-government or private orphanages that are partly funded by government grants, specifically grants from the Ministry of Social Welfare, and partly by charitable and philanthropist donations.” > source

Partial information: “There are no statistics regarding the actual number of children in welfare institutions in Bangladesh. The Department of Social Services, under the Ministry of Social Welfare, has a major programme named Child Welfare and Child Development in order to provide access to food, shelter, basic education, health services and other basic opportunities for hapless children.” (The following numbers mention “capacity” only….not actual numbers of orphans at present)
9,500 -State institutions 
250 -babies in 3 available “Baby Homes”
400 -Destitute Children's Rehabilitation Centre
100 -Vocational Training Centre for Orphans and Destitute Children
1,400 -Sixty-five Welfare and Rehabilitation Programmes for Children with Disability > source

“The private welfare institutions are mostly known as orphanages and madrassahs. The authorities of most of these orphanages put more emphasise on religion and religious studies.” One example follows: 400 – Approximately - Nawab Sir Salimullah Muslim Orphanage > source

Read “Women and Children in Disadvantaged Situations.” Odhikar. (4/2001) > source