For Palma see here...
http://www.consorcidetransports.org/web/ctm/autobus/seccio/500
...you can get a bus, the 501, from Cala Egos to Palma then change to a local out to Playa De Palma.

For Puerto Pollensa, see here...
http://www.consorcidetransports.org/web/ctm/autobus/seccio/400
...you can get a bus, the 448, from Cala Egos to Puerto Pollensa. Although it looks to me like it takes almost 5 hours so you will be quicker going to Palma then change to the 340...
http://www.consorcidetransports.org/web/ctm/autobus/seccio/300
Get a timetable by clicking on the number 448 then on the next page click the PDF at the bottom left. That applies for any of the bus route numbers.

All timetables for Mallorca are here...
http://www.consorcidetransports.org/web/ctm/21
...select the line you want to the right of the map at the top left. Click the Union Jack at top right for English.

Thanks for the info Pollensa 1946,do you know if it is possible to buy " a day pass " for the bus?

Regards Alan

Day pass... If you go here...
http://www.consorcidetransports.org/en/web/ctm/inici
...then click "Fares" you will get details of multi-journey cards (known as the Inter-Modal Card). Although I am sure you can only buy them at major stations, such as the Plaza Espania in Palma. Check with Tourist Info in Cala Egos/Cala D'Or.

Thanks for info and help Pollensa 1946, i have just got the info as have been off line due to decorating and had to shift computor.

Regards Alan