A proposed pedestrian and bicycle bridge linking Rosslyn and Roosevelt Island will be the subject of several federal hearings to be scheduled this fall.

The proposed bridge would span the George Washington Memorial Parkway.

Currently, no funds are available for the bridge, which has been in the planning stages since the mid-1970s and is expected to cost $670,000 to $970,000.

The bridge, as now proposed, would connect several major bicycle trails and provide a new pedestrian and bike route across the Potomac River on the sidewalks of the Roosevelt (I-66) Bridge. Its design would be similar to pedestrian bridges over the Maryland section of the parkway along the C&O Canal near Glen Echo.

With the required environmental review in process, the bridge's location and design still need the approval of county officials, the National Park Service, the Fine Arts Commission and the National Capital Planning Commission.

A public hearing will be held sometime this fall, before the final environmental review is issued. Additional hearings are expected this winter before the Fine Arts and National Capital Planning commissions.

But even if the bridge is approved by all of the agencies, there is no money to build it.

Arlington County voters approved $250,000 for the bike and pedestrian bridge in a 1977 highway bond referendum. But that is only a fraction of the escalating construction costs and county officials don't know where they will get the rest of the money.

Virginia's Commission on Outdoor Recreation two years ago said it might help fund the project with federal park grants received by the state. But for the first time since 1965 there may be no federal funds next year to help states acquire and develop park land. The Reagan administration has opposed the creation of new parks and has asked Congress to end Land and Water Conservation Fund grants to the states, an issue Congress is debating this week. The state presently contributes no money of its own to develop parks in Virginia.

Park Service officials said last week that because of budget cutbacks, they also have no money to help build the bridge, which would be on Park Service land.

The bridge would connect with the 16-mile Mount Vernon bike trail, the Rock Creek trail across Roosevelt Bridge and a trail now under construction along I-66. The I-66 trail, to open next year, will connect to Northern Virginia's longest bike trail, the W&OD which extends to Loudoun County.

The environmental assessment for the proposed bridge, required under federal law for projects on park land, focused on three locations. It initially concluded that the best site would be near Roosevelt Bridge, although it would cost about $35,000 more than a bike bridge crossing closer to Key Bridge.