Starting Monday, passengers on many Metrobus routes will have to exit by the front door as Metro gears up a new system to catch bus fare evaders and collect the estimated hundreds of thousands of dollars they avoid paying each year.

The system, which has been advertised on Metrobuses for weeks, was designed by a committee of Metro bus drivers in cooperation with the Metro board and will be most noticeable to riders on long-haul suburban routes. It should have less impact on inner-city short-trip passengers. The major inconvenience that the thousands of honest Metro patrons will experience every day is that they will no longer be able to get out the back door of a standing-room-only rush-hour bus if that bus has crossed the boundry of one of Metro's suburban fare zones.

In the District of Columbia, where there are no fare zones, those taking advantage of the system will find it a little bit tought -- but not impossible -- to pass on an unneeded bus transfer to a friend so that he might ride free.

Fare evaders, mostly suburbanites according to consultants who have studied Metrol, are costing the transit authority "hundreds of thousands of dollars a year," in the words of assistant Metro General Manager Nicholas J. Roll. Nobody is willing to make a more precise estimate.

Most abuses occur, according to Metro officials and drivers, when riders board a bus in one zone, pay the fare for a one-zone trip, but actually ride the bus to two zones or three zones. Depending on the zones, the loss to Metro per trip can be as much as 60 cents. The driver has no way of checking how far the rider rides, thus accepts the rider's word that he is traveling the shorter distance.

"They're laughing at us," one driver told the Metro board, "and we're tired of it." Drivers are under considerable management pressure to extract that correct fare. They complained during their wildcat strike in July 1978 that they did not have the tools to enforce the fare structure.

Beginning Monday when riders board a bus that will cross zone lines, they will be issued a slip of paper that indicates where they boarded and what zone they paid to. Then, when they reach their stop, they will have to return the slip of paper to the driver as they get off at the front door. The back door will remain locked.

The problem will come on those packed rush hour buses where a standee caught on top of the diesel engine in the rear has to fight 40 feet forward to the front door through dozens of other standees to get off.

"We expect some confusion the first day but we think people will get used to it," said Leroy Bailey, general superintendent of Metro's bus operation.

The slip of paper that acts as a zone check will also be used as a transfer for those patrons needing to transfer from one bus to another.

Coupons on the slip will be torn off at each transfer point until a total of three transfers have been made. Three is the maximum number of free transfers Metro permits.After the third a new full fare must be paid.

The new slip of paper will be punched by drivers to show the pertinent fare and zone information so subsequent drivers will not over- or undercharge the rider.

The zone check system is not new to the Washington area; it was used by both the old privately-owned D.C. Transit system and AB&W company in suburban Virginia before Metro acquired them and two other bankrupt bus companies in 1973. Similar zone checks are common in other transit systems.

In printing the first month's supply of new slips of paper, Metro made a mistake. The top third of the slip contains hour-and-minute information which the driver is supposed to punch in such a way that it shows when the transfer expires. However, a printing blunder makes it appear that the transfer will be valid for the rest of the day no matter where it is cut.

"That slipped by all of us," Bailey said. "We're fixing it."