Greyhound Turns Back the Clock on Fares : Transport: Struggling carrier targets long-haul passengers, who usually opt for the airlines.

Greyhound Lines Inc. will slash long-haul fares as much as 38%, to year-ago levels, in the hope of spurring traffic and raising cash before the slow winter season.

Greyhound will reduce the fares on trips of more than 500 miles--those on which most travelers prefer flying to taking the bus.

For example, Greyhound lowered the one-way, walk-up fare between New York and Denver to $99 from $159, a 38% savings. Other new one-way fares include Washington to Los Angeles, cut 37% to $119, from $189, and Miami to Dallas, reduced 34% to $99, from $149.

Dallas-based Greyhound will also offer a three-day advance-purchase discount of 25% off all fares for trips taken before Dec. 15. Greyhound already offers a 35% discount for seven-day advance purchases.

The new fares take effect Tuesday. Walk-up fares have no advance-purchase requirements.

Greyhound’s stock was off 12.5 cents at $1.94 on Wednesday on the New York Stock Exchange. Volume was 177,200 shares.

Through Dec. 8, the company is also promoting a “Buy One, Get Home Free” offer on round-trip tickets bought seven days in advance for travel through Dec. 15. The return portion of the trip is free, Greyhound said.

Pinched by competition from low-fare airlines, the carrier expects to complete a restructuring by the end of the year that will allow it to avoid Bankruptcy Court protection.

In the first nine months of 1994, the number of travelers on Greyhound fell 4.1%, to 11.1 million from 11.6 million.

Greyhound is the only nationwide bus company. It serves more than 2,600 destinations with a fleet of 1,898 buses.