If Bea was down there thru a secret tunnel how did her horse climb that ladder to get outside?
(psst. it's not really a horse, it's a unicorn, with wings. they can fly.
)
actually: i don't think there's any indication that she was the one riding the horse. the stirrups are put in a place where either patchy or bea could have been riding it. (i don't buy the whole "to short for a tall person to ride") Plus why didn't she run instead of risk being found?
for whatever reason (location/time of day/etc.) i don't think she was worried about being found. plus, remember i don't think she neccissarily was riding the horse, i think she could have gone through the underground tunnels. 
Why didn't Kate/Sayid find said secret tunnel?
it was behind all the dharma jumpsuits. in the back of the closet. that's where all secret entrances are hid. bea showed up before they could open it.