Bournemouth is easier to reach than most of the Dorset coast, which is a large part of why it grew into the town it is. Everything below assumes you are arriving for a stay rather than passing through.
By train
There is a direct service from London Waterloo run by South Western Railway, taking around two hours, with trains through the day. Bournemouth station sits a short distance inland from the centre — walkable to the town, and a longer walk or a short bus ride to the seafront.
The line continues west to Poole and beyond, and east towards Southampton, so both towns at either end of the bay are reachable by rail as well as by bus.
Check current times and fares with the operator before travelling; timetables change and engineering work is common at weekends.
By coach
National coach services run to Bournemouth from London and other major cities. It is slower than the train and usually cheaper, and the coach station is close to the railway station.
By car
Bournemouth is reached from the M27 and the A31. The drive is straightforward; the parking is not, at least in summer.
Central and clifftop car parks fill early on hot days and are effectively full during the Air Festival weekend in late August. If your accommodation includes a space, the sensible move is to leave the car in it and walk. If it does not, parking inland and taking a bus in is faster than circling the seafront.
By air
Bournemouth Airport lies a few miles north-east of the town near Hurn. It is small and serves mainly holiday routes, so most people flying in from further afield arrive at Southampton, Heathrow or Gatwick and continue by train or coach.
Getting around once you are here
On foot. The promenade runs the full length of the bay, flat and uninterrupted, from Alum Chine in the west to Hengistbury Head in the east. It is the single best piece of infrastructure in the town. Pier to pier — Bournemouth to Boscombe — is about half an hour.
By bus. Local services run frequently along the main roads and connect the neighbourhoods, the town centre, Poole and Christchurch. This is what makes a car-free stay genuinely workable.
By bike. The promenade is cyclable, with seasonal restrictions on the busiest central stretches during peak summer hours. These are signed and they change, so read them rather than assuming.
Cliff lifts. Several Victorian funiculars still connect the clifftop to the promenade. They run seasonally and have had spells out of service, so treat one as a bonus rather than a plan.
More
Getting around without a car goes into the practicalities in more depth, and the map shows how the whole bay fits together.