Hi Charlie. Fellow Bristolian here, (Westbury on Trym, but mostly lived in Cornwall).
Whilst I'm not too keen on Salitre area myself, Its often good to live close to where you'll be working, for travelling each day, morning and night can be awful, especially in rush hours.
Personally I much prefer Cedritos/Mazuren areas, in the north of the city. They are cleaner, greener, quieter, less traffic, less pollution, and in my own opinion, less crime too. They are areas where a lot of middle class families live, better quality of life, better housing, etc, whilst not too expensive. But as I say, travelling every day to work isn't too good.
But wherever you choose, DO make sure you find a place close to the Transmilenio, which is a rapid transport system of articulated buses that run on designated lanes, free of other traffic. This is not only advantageous for work, but for getting in and out of the city for nightlife too. Fares are cheap, you can go the whole length of the city, from the furthest south, (not that you would want to go to those areas, - can be very dangerous) to the furthest north, probably about 30 kilometers for a mere 2,000 pesos, about 55 pence. Normal buses get clogged up in the traffic jams, and doubles or even trebles your journey times. Taxis, whilst pretty cheap, also get stuck in the jams, but their meter continues clocking up whilst sat in a jam for an hour. That makes them expensive. Taxis are ok at night, and I recommend you use them at night, as they should be safer.
Now, how to find a place ...... Most flats come unfurnished, and any that you find furnished will be a lot more expensive, and so if you are there for only a year, buying furniture is something you don't want to do. So the best option is to flat-share. You should look for "habitaciones", which is usually your own room, but sharing the rest of the apartment with other like-minded people.
I find that the best place to look is the national daily paper, El Tiempo.
Along the options bar at the top of the page click on "Classificados", then in the column Venta y Arrienda de Vivienda, click on "Ver m獺s en Vivienda".
Then in the second column, for stuff in Bogota rather than the whole country, click on "Habitaciones en Arriendo en Bogot獺". This will bring up all the flat-shares.
There is a menu on the left hand side where you can filter according to what you want.
This is probably the most up to date list that you'll get. On other mediums they rarely update them, so some places will have properties that were filled months ago. I wouldn't bother with AirBnB, Craigslist, etc, for they are usually only used by Americans, and if anyone advertises a flat on them, they will be "Gringo prices", targeting rich Americans, and a total rip-off.
Good luck.