TO the coo of birds and the bubbling of streams, add one more sound of an Alaska summer - the jingle of bear bells. After two people were killed in a bear attack on the outskirts of Anchorage, Alaska, hikers tromping through the Chugach Mountains here have begun wearing the noisemakers to warn animals of their approach. Others have taken to carrying pepper spray - or even guns. ''We really don't have any hard-core analysis of 'bearanoia,' but I think it's there,'' says Al Meiners, superintendent of Chugach State Park. Alaska's largest city is home to about 40 black bears and an estimated three to six brown or grizzly bears, says Mike McDonald, a state Fish and Game biologist who conducts bear-safety seminars each summer. There is evidence that the bear population has grown recently because berry crops in the past two summers were especially good. But Alaska is not alone in pondering the mixed blessings of increasing bruins. * In western Massachusetts, the black-bear population has soared from about 300 in 1980 to about 1,300 today. A summer drought has forced berry-eating bears to rummage through garbage cans to survive. Some have been sighted as far east as the Boston suburb of Acton. * In New Hampshire, state authorities have extended the hunting season in northern counties, where the majority of the state's 2,500 bears live, to help thin the population. * In Maine, where bears number 21,000, a family in Cardville hopes that the upcoming bear-hunting season will end the siege of a trio of bears near their home that has left them virtual hostages. Despite the heightened fears in urbane Anchorage, bear attacks are rare, says Mr. McDonald. Since 1900, 28 people have been killed by bears in Alaska; by contrast, 29 Alaskans have been killed by dogs since 1975. As of late July, 10 bears had been killed by Fish and Game or by residents to defend people or property; the previous summer high for such killings was seven. Part of the problem in Anchorage may be the increasing popularity of local mountain trails for Anchorage runners and mountain-bikers. Some officials worry that trail-runners, who travel quickly and with their eyes on their feet to avoid tripping, are at special risk of surprising bears. ''I always tell people trail-running's dangerous,'' said Jerry Lewanski, chief ranger at Chugach State Park, following the fatal July bear attack on Marcie Trent and son Larry Waldron. ''They're doing all the things I tell them not to do when they're in bear country. Being quiet and silent is the worst thing to be.'' The recent bear scares have stimulated discussion of reopening hunting on Anchorage's rural edge, McDonald said. Yet many Alaskans remain fond of their bruins - if at a distance. A campaign by environmentalists will effectively reduce hunting in the area adjacent to the McNeil River State Game Sanctuary, a reserve that holds one of the world's biggest concentrations of grizzlies. When the Alaska Board of Game decided to allow hunting near the sanctuary, a group called Friends of McNeil River encouraged nonhunters to apply for fall bear-hunting permits. The campaign was successful. Six of the eight people who won hunting permits for the area - awarded by lottery - are nonhunters.