Are children allowed to travel alone?

It depends on bus company and children's age. In some cases a written authorization from a parent or legal guardian is required. Child must have a valid ticket and all required travel documents. Minor should also be picked up in the arrival location by a parent or legal guardian.

Minor's travel

Bus companies allow underaged children to travel, but carriers from different countries may have various regulations and be subject to different law. If you are a minor or a parent/legal guardian and want to travel or send your child alone, please contact your company's office for more details on such journey or read its Terms and Conditions.

Find below rules of minor's travelling from most popular European bus companies:

National Express

Minor passengers must be aged over 14 to take their journey alone. Bus driver may demand an ID or other document for proof of age. For passengers travelling without an escort - over 16 years old only - on board of National Express Eurolines bus, a letter of authority is required from a parent or legal guardian.
source:National Express Terms and Conditions, dated - 09.12.2016

Flixbus

For passengers under 10 a presence of an adult is required on all domestic and international Flixbus services. Minors between 10 and 14 years old can travel alone only if their parent or legal guardian provides the company with a letter of authority. This doesn't apply to overnight services, which are crossing any border or to services with an interchange.
source: Flixbus Terms and Conditions, dated - 09.12.2016

Eurolines France

Children under 16 must be accompanied by an adult, if this adult is not the parent or a legal guardian then a letter of authority from one of them is needed. Minors over 16 years old are allowed to travel on their own.
source: Eurolines France Terms and Conditions, dated - 09.12.2016

Sindbad

Children over 12 years old can travel alone but only with a letter of authority from a parent or legal guardian. This does not apply to international routes to and from Italy, Greece, Bulgaria UK and Ukraine. Copies of ID's from parents or legal guardians may be required.
source: Sindbad Terms and Conditions, dated - 09.12.2016

For more detailed information on minor's travel, please contact your bus company's office or read their Terms and Conditions.