I noticed that Amtrak has a bus which transfers folks from Ashland to the Amtrak Train San Joaquin Valley Train Route. The unstaffed bus stop is at the Safeway Parking Lot. There's a sign there with fares and schedule, but I recommend contacting the link below.
The city of Ashland and the Southern Oregon University are committed to subsidizing low fare good value bus service in town. Fare in town is only 50 cents, and Senior Citizens and Youth from 11-17 pay only 25 cents. Children 10 and under pay nothing. There is also service to Medford for the price of $2- provided by the Rogue Valley Transportation District. See link below for more details.
I-5, one of the largest freeway routes in the world stretching between San Diego and Seattle, reaches its highest elevation at the Siskiyou Summit, which is just a couple miles south of Ashland. Be especially careful when driving over this summit whether it be summer or winter. In summer, any vehicle with a weak engine will boil over and ANY vehicle, even with good brakes, can face brake failure. Some roads in the European Alps may compare with this long 6% grade climb/descent, but I've never seen anything like it in Appalachian Mountains. Because of the generally excellent grading, and wide surface, drivers are tempted to drive faster than is safe, so follow the warning signs carefully. Note the speed sign set for various weights and how slow those speeds are. In addition, this route is a primary artery for big rigs hauling loads between Seattle and San Francisco, so automobile drivers should stay well away from trucks. In particular, don't get in front of a truck on the downhill slope because their brakes can and do fail. They need maybe two truck lengths of space in front as a safety margin. On the uphill slope, prepare for very slow trucks in the right lane, especially at night. When climbing hills, truck drivers depend upon forward momentum during gear shifting, so avoid impeding and frustrating a driver by driving too slowly in front. Get up and away from big rigs. In winter, bring chains and prepare to drive on them. The Siskiyou range is not too many miles long, but these steep grades require chains frequently during winter. There are places on the roadside for putting on chains, and for a fee you can get help. Chains are no substitute for dry asphalt though, so use caution and avoid those truckers. There are runaway ramps padded with sand, but you won't want to use them--they will trash your vehicle. The link below provides more general information about the Siskiyou Mountain Range, of which Mount Ashland is the tallest at 7,533 ft/2,296 m.
Although it's not well publicized, there is a convenient way to travel via AmTrak train to and from Ashland, Oregon. An AmTrak bus picks up passengers near downtown Ashland and transports them to AmTrak in Sacramento, CA. From there, a traveler can connect to nearly anywhere. Check the AmTrak website for info.
Ashland is just off the major north-south freeway, Interstate 5. It is 15 miles from the Medford-Jackson County International Airport, where rental cars are available. Not much local transportation is available.
On foot, for the heart of town. Traffic can get pretty congested. Otherwise, a car is almost necessary. There are several companies which offer excursions to Oregon Caves, the Rogue River, Crater Lake, Jacksonville, etc.