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The mathematics of close linebreeding 
Call our star bitch “A”.  Remembering that each puppy is ½ of each parent, her half-sibling offspring would all be 50% A, and 50% of the unrelated sires; we’ll call them B and C. So we can describe the offspring as ½A½B and ½A½C.  
If you breed these two half siblings, the puppies each get ½ of their genes from each of their parents, and doing the algebra, we see that the puppies from that linebred cross are ½ of (½A½B) plus ½ of (½A½C), coming to ¼A¼B¼A¼C. Adding up the fractions, you will see that the puppies are only ¼ each of the less desirable sires B and C, but are still at ½ of our very desirable bitch A. And when you breed those puppies to another “A” line out of unrelated sire D, they come up to be ½A,1/8B,1/8C,¼D;  and they will still be at 50% of A.  
By starting with half-siblings, out of otherwise unrelated lines, we can breed forward endlessly, and still stay at 50% of our desirable bitch A. This is actually easier if the outstanding individual is a dog, as you can create many half-siblings within the same generation, but as you can see from our bitch "A" example, it is still possible to line breed with a bitch, just slower to get started.  
The key to working with a bitch would be to breed her to a different dog every time, and to hang on to the half siblings. You will then be able to start linebreeding, all at that magical 50% of “A”. Note that if we breed back a generation, for instance dog AB back to bitch A, we have then crossed over into inbreeding, resulting in an animal that is 75% A and 25% B.  Anytime the percentage of any one animal goes over 50%, you are inbreeding; by definition, line breeding will never take you higher than 50%.  
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Inbreeding 
Inbreeding is mating the dog to one of its immediate ancestors without introducing any fresh blood at all. Although it is extremely useful in telling the breeder what faults may be hidden in his strain, and also fixes the virtues, which may outweigh the faults, inbreeding should only be used by extremely experienced breeders who know their dogs in and out for a longer period of time, and then only if absolutely necessary for an essential fact.  
When dogs are inbred haphazardly, without culling of inferior stock, many undesirable traits may become predominant in their offspring. For example, the inbred dog's ability to resist disease and his overall performance capacity are often depressed. The growth rate of the inbred puppy, and the average mature size within the inbred litter, frequently decreases. Nonselective inbreeding is directly related to a depressed fertility rate, an increase in abortion and stillbirth. Some basic principles of genetics show why these traits are directly related to inbreeding. 
Closebreeding, a breeding system which uses extreme inbreeding, such as mating between siblings or between parents and offspring, is also sometimes used by experienced breeders, but again has its risks and should only be resorted to for a very good reason.  
Inbreeding and closebreeding are riskfull breeding systems, and in a time when culling your litters was common practice it was easier to get rid of the undesired results. Nowadays you will be dealing with your vet in any event when it comes to euthanasing any pup. Some vets are 
not prepared to euthanase in all instances; for example, if they are of the opinion that too much white is not a satisfactory reason they might very well decline your request. And unfortunately there are commercial breeders who will refuse to cull their litters at all, because every puppy, even a bad one, is a source of income.   

Outcrossing 
When outcrossing you introduce a dog that contains none of your own strain whatsoever and none or very few of the names appearing in your bitch's 4-generation pedigree. You would only outcross if you're not satisfied with your own strain at all. Crossbreeding initiates the desired change, while inbreeding or linebreeding increases the ability of each generation to breed "true to type". 
The chances of getting something good out of an outcross breeding are remote. However, if the breeder is planning ahead, this may merely be a step in a longer term strategy. For outcrossing to work, the next logical step is to breed close again to the line.  
When you outcross you basically leave it up to great randomness about what the puppies will look like. You will NOT get the best charactertics of the mother and the father. In all likelihood, you will get a very average looking litter or worse.