Hi, Fool, sorry to hear this. Did you adopt from a rescue in the UK? It's virtually unheard of for a rescue not to spay/neuter before adoption goes ahead.
We went through something very similar with a foster bitch recently, and she is staying with us till she has her spay op in mid October. The bitch will be bleeding for around a week to ten days. We just gritted our teeth and kept cleaning - fortunately our downstairs is quite dog friendly, and not too much of a problem. I believe you can get dog nappies - a sort of padded towelling affair that the bitch can wear - have a look on Google. If this is the only season she is going to have with you, and the only unspayed bitch you have/will have, it may not be worth the expense/bother, but I guess it depends on your attitude to mess as well. We certainly didn't find it too onerous and we wash things like dog beds very regularly anyway.
It's very important your bitch is NOT exercised around entire males for at least three weeks. After the bleeding dies down, is when she is at her most receptive, and we found that even our neutered males were very interested and there were lots of attempted humpings. 
You will need to either confine her to the garden or find somewhere very secure to exercise her. You should also bear in mind that male dogs will be able to smell her from at least a mile away, so please ensure your back garden or anywhere she goes for a wee is VERY secure, and no Romeos can break in/jump over walls/tunnel under.
We erred on the side of caution and did not resume full "social" walking till four weeks had passed, though by then she was going out regularly very early in the morning when nobody else was around. It's also an idea at the end of the season to ensure all soft furnishings and the dog are given a good wash/bath to remove any lingering traces of scent. Once season has finished, you then have to wait around three months optimally to have her spayed. Is the resuce contributing to the cost of this?
The reason for this delay is the dog's cycle, and after the season, there is still a lot of blood flow around the uterus. As hormones decrease, blood flow decreases so three months on, is low point of cycle when safest to spay. However, what you should also be aware of is after season, is the danger time for pyometra, an infection of the womb, which is lethal. Unspayed bitches are most at risk, and risk rises with age/number of seasons. Keep a VERY close eye on her and whisk her to the vet if you see any discharge, or she is off colour/high temp once season is finished.
For secure dog exercising, see if your local greyhound charity can recommend somewhere (most have somewhere secure off lead you can use), try a dog training school, or the other option is a local riding school - if they have an indoor manege, this would be perfect as secure with a good floor. Many riding schools are happy to hire out for an hour especially during week days when business is quieter.
I know it feels like a faff when it happens, but it really is over very soon.
Good luck 