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Bot eggs are not ingested.  The warmth and moisture from the horse's lips 
rubbing on them make the eggs hatch.  (The empty egg cases actually stay on 
the horses legs.)  The first instar bot then makes its way from the horses 
lips into the mouth.  I believe they live in the mouth for a couple of days.  
They then molt and migrate down into the horses stomach where they can live 
for about a year.  When they are in their pupal state they pass out through 
the manure and after a few days hatch out as winged adults.  The adult life 
span is very short (a couple of days).  Adult bot flies are unable to eat.  
They just mate and the female lays her eggs.
If you've ever seen a female bot fly laying her eggs it is quite interesting. 
 They look like honey bees, but the abdomen (ovipositor) turns down.  She 
flies around the horses legs and seems to check out the "best" place to place 
her eggs.  My theory was that she places them only where the horse can reach 
them with its mouth.
Actually the best way to treat bots is to remove the eggs after they are 
deposited on the horse and before they are ingested.  When I was in graduate 
school I did a project of hatching out bot eggs.  I found that they did/could 
not hatch until about 2 days after being on the horse.  So in theory if you 
can remove the eggs at least every 2 days your horse will never gets bots 
internally.
In watching the females lay eggs the same female lays up to a couple of 
hundred within a few minutes.  So if you just follow behind and remove them 
they are gone and so is the risk of them ingesting them. Unless you are in a 
very heavily infested area it's quite unlikely that another female will lay 
eggs for another few days.
The best tool I have ever found is called a bot egg remover.  I've had it for 
over 20 years and it just zips them off quickly, with nothing left behind.  I 
do NOT recommend the idea of washing the horse's legs with warm water to make 
them hatch.  For one thing, you don't know if they were all "ready" to hatch, 
so some eggs might remain that could hatch later and be ingested by the 
horse.  The other thing is that the eggs casings still remain and you still 
think you have a bot problem.  The material the female uses to adhere the 
eggs is quite tenacious and not easy to remove by washing. 
Now that my horse lives where the surrounding horses are very well cared 
for...de-botted and treated with wormers on a regular basis I rarely even see 
any bot fly eggs on him.  Bots are pretty much the least of my worries as far 
as parasites go.
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