A key Senate subcommittee yesterday endorsed a proposal to further reduce the number of passengers permitted to use National Airport and voted to study a plan to set up a helicopter shuttle service linking downtown Washington to outlying Dulles and Baltimore-Washington International airports.

The Transportation Appropriations subcommittee proposal calls for either lowering the current cap on passenger use from 16 million passengers a year to 14.8 million by 1985 or freezing the cap at its current level. Both measures are designed to channel future growth to Dulles and BWI.

The Federal Aviation Administration says National's current use is 13.5 million passengers a year.

Last month, the House blocked a proposal by Secretary of Transportation Elizabeth Dole to limit the number of passengers allowed to use National to 14.8 million.

Dole said yesterday that she is pleased that the subcommittee's action "will allow us to continue with our rulemaking proposal to lower" the passenger cap at National.

She said she is confident the measure will be approved by the full committee when it takes up the issue Thursday. Sen. Paul S. Trible Jr. (R-Va.), who has lobbied for a lower passenger cap, said the subcommittee's action reflects the view that National's growth must be controlled. "Safety, noise and economic considerations dictate that Dulles airport be more fully ultilized and some limits be placed on passenger growth on National."