Social services

I'm bringing my new Schnoodle puppy home in about five weeks time. I want to take her out and about to socialise her as much as possible, but I'm not sure which establishments she will be allowed in. I know that food stores, restaurants etc are out of the question but can I take her into banks, newsagents, hairdressers etc? Providing there isn't a sign on the door saying 'no dogs allowed' can I assume it is okay? I'm also unsure about public transport. Presumably she will be able to come on the train with me (does she need a ticket?) but what about buses?
I live on my own and will be the only one going out with her, so I won't be able to leave her with someone outside the shops. I do see some dogs fastened up outside shops but I wouldn't want to leave her on her own in case someone decided to take her.
Any advice you can offer would be much appreciated.
Sheila Whetnall, by email