International Bank of Washington yesterday reported its first-quarter profits dropped to $3.6 billion (29 cents a share) from $4.8 million (29 cents) in the same period a year ago.

The Rouse Co. of Columbia, posted slight gains for the quarter in both net income and earnings before depreciation of its extensive shopping center properties.

Rouse said its net increased to $659,000 from $624,000 and earnings before depreciation allowances were up 7 percent to $3.2 million from $3 million for the three months ended March 31. Rouse did not disclose earnings per share; the company reports earnings before depreciation because it says that figure more accurately reflects its performance.

Rouse said all its operating divisions, except its mortgage banking operation, showed improved earnings for the quarter compared with the first quarter of 1980.

The company announced plans to buy the Randhurst Shopping Center in the northwest suburbs of Chicago and said it will open five major projects this year, including White Marsh in Baltimore County and an addition to The Mall in Columbia.

American Indian National Bank reported record earnings of $249,000 for the quarter ended April 30, up from $113,000 in the same period a year ago. The bank, which is owned by American indian tribes native Alaskan corporations and individual investors from the two groups, said deposits have more than doubled in the past year, from $12.3 million to $25.4 million.

Bowl America Inc., reported record third-quarter profits of $731,000 (54 cents a share), up 20 percent from the $622,000 (45 cents) of the same period last year.

For the first nine months of its fiscal year, Bowl America earned $1.14 million (84 cents), compared with $1 million (73 cents) last year.

Revenues of the 26-unit, Springfield-based bowling center chain increased from $4.6 million to just over $5 million for the quarter and gained from $11.3 million to $12.2 million for the nine months.

Bioshperics Inc. of Rockville reported its first-quarter net dropped to $15,900 (1 cent a share) from $57,000 (4 cents) last year, while revenues declined slightly to $1.42 million from $1.45 million.