BDM International Inc. profits jumped 63 percent in the third quarter and 48 percent for the year to date, reaching record levels.

Third-quarter earnings for the McLean-based diversified professional and technical services firm were $1.2 million (55 cents), compared with $758,000 (34 cents) last year. Revenues for the latest period were $32.5 million, compared with $22.6 million last year.

For nine months, BDM earned $3.2 million ($1.42) on revenues of $83.9 million, compared with $2.2 million (97 cents) on revenues of $64.1 million in 1981.

Catalogue showroom retailer W. Bell & Co. Inc. posted a loss of $134,100 during its first quarter ended Sept. 25, compared with earnings of $126,800 (7 cents) last year. Sales by the Rockville-based firm slipped to $22.4 million from $23.8 million.

Essex Corp., a professional services firm headquarterd in Alexandria, reported net income more than doubled in the third quarter.

Third-quarter earnings were $105,198 (9 cents) compared with $49,904 (7 cents) in the comparable period last year. Revenues increased from $3 million to $3.6 million.

For the nine months, Essex posted net income of $336,446 (30 cents) on revenues of $11.3 million, compared with net income of $201,472 (30 cents) and revenues of $8.8 million a year ago.