Hi
I'm Asian, female and will be travelling solo in Andalucia (Seville, Cordoba, Las Alpujarras) and Madrid.
I'm not into night life so am not likely to wander the streets after an early dinner. However, I'm an early bird and usually ready for sightseeing by 7.30am. I enjoy taking photos and the camera is inevitably visible wherever I go.
Would appreciate feedback on the safety of each place and any area I should take care to avoid.
Also, I would be travelling by bus extensively. How reliable is the bus service and can I count on the time schedule provided on the website?
Thanks!

Madrid is a pickpocket's paradise.
Nothing can or will be done for victims. Its a waist of time for the cops. Tourists can't wait around for the trial, if the guy is caught. And he won't be. Its a systim. The bad guy hands off the loot to a henchman, who quickly disappears into the crowd. Nothing can be retrieved or proven.
And there's a hungry market for stolen passports too.
I use Rick Steves' money belt that holds passport, plane ticket, and other things listed in the funny instructions. Mine saved my.., 3 times.
( I should have a rubber stamp made if this warning. I print it so often. )
www.ricksteves.com

An early dinner in Spain is at 20:00 rather than 21:00 or later. Restaurants with dinner earlier than 20:00 are hard to find.
Hmmm, many restaurants in Andalucia don't open their kitchen till 8:30...I think the OP meant 7 in the morning anyway.
How big/high tech is your camera? Do you carry a camera bag or do you stick your camera in your purse?
I found only a few areas of Madrid to be of concern - Puerta del Sol is a hell hole as far as I am concerned, and unless you want to photograph tourists there is very little of interest there. Early morning is an excellent time to take pictures and wander around. I really can't imagine anyone will bother you at that time, the streets should be fairly empty still.
I'm female, I travel alone a lot, I take photographs as well and I have never been bothered, had my camera stolen or my pocket has never been picked in all of the 10 or so years in Spain. Just have your wits about you and you'll be fine.

Maybe you know it already, but there isn't an "only" bus company in Spain: you have to know where are you going and which company gets there. When you're in the place, check the timetables at the ticket's office: sometimes what you find on the internet is old or season information.
Okika,
You shouldn't worry about safety any more than any other place. Use common sense as you would at home or in other cities. Pay some extra attention to pickpockets, though; get a money belt.
You'll love Andalucia; your camera will too. While in Sevilla, be sure to see the Alcazar: beautiful mozarabe architecture. Also visit the Plaza de Espana where part of one of the Star Wars movies was filmed (that's not the only reason to visit it, of course, I just thought i'd mention it); it's very photogenic. Also, La Mezquita in Cordoba and other places there.
Part of Dr. SZivago was filmed at Plaza de Epaña too. Early morning is a good time for photos. Interesting shadows.
Seville is a safer than average town, due to an extensive all volunteer neighborhood watch.
They busted up a Morrocan gang who was causing the street crime, in 2003.
Other than that you may get run down, by a horse who's watching girls, like the rest of us.
Man, the horses, drawing carrages are magnificent here too.
Getting around early shouldn't be a problem I think (watch your belongings, but that goes without saying, defenately buy a moneybelt or something). Andalucia and Madrid are perfect to photografing. You'll have a blast! Between the hours of 1.30 and 5 pm, most shops are closed (in big cities this is not the case for the bigger shops) and things will be quiet (it's also hot at that time), so maybe you can adjust your pace? I mean, during this time you can stroll around in peace and take piccies during the daytime. Or you can wait untill after 5, take late-afternoon and evening pictures and have dinner around 20.30 (the Spanish eat very late, 21.00 at th most early and mostly tapas or a small meal as they have their big meal during siësta.
Either way: embrase Spanish life, you'll love it.
Oh, despite it's reputation, I find the Spanish public transport to be rather accurate. THe trains are anyway and I haven't had that much of a delay with busses.

Thank you everyone who has responded to me - I really appreciate all advice.
NavajoRug, I'm using a digital SLR which usually hangs around my neck plus a manual camera (which I'll time and again dig out from a shoulder bag). Chances are I'll take a heavy lunch around late afternoon which doubles up as dinner plus small meals /snacks from breakfast to then :P
I don't usually wear a money belt, rather I have a pouch hung around my neck, tucked under and pinned to my shirt/blouse (that should be ultra secure, I believe??)
And yes, I'm really looking forward to visiting Spain and hope to snap some really glorious photos.
I'm not a fan of money belts but that's a personal opinion. I just really hate having that small boa constrictor with money in it squeezing my waist.
I've found that it is easier to carry a dedicated camera bag than having to rummage through million things to find it, the less distraction, the less chances a thief/pickpocket has. People seem to react better to a high tech professional looking cameras than to small ordinary ones. Go figure :)
I hope you have fun and come back with beautiful photos.