"Было" in these sentences is a particle, not a verb.
It can be roughly translated as "almost, about to, nearly, on the point of, just about to".
The meaning of this particle is that the action (expressed by a verb that is followed by the particle "было") was started, but wasn't finished or hasn't succeeded.
Let's take a closer look at your examples:
-Правду сказать, я не уверена... -начала было Мод, но миссис Барнард уже выскользнула в прихожую и направилась к лестнице на второй этаж.
Here, "было" refers to the action of starting (to say): начала было. So the woman started her sentence, but didn't finish. The particle "было" adds a meaning of interrupted speech and of changing her mind.
Я схватил наволочку (вместо мешка для конфет), и мы с Роули направились было к выходу.
In this sentence, "было" is situated after the verb "направились". So the narrator and his friend started to walk towards the exit — but something stopped them. (Look at the next sentences for more context)
Папа попытался было отмазаться, но, если мама чего-то решила, шансов, что она передумает, - никаких.
The father tried to make excuses — he even began to explain himself, but it was in vain. So his actions didn't succeed, because the mother had made her mind already.
После этого мы собрались было дальше, но часы показали половину одиннадцатого: поворотное время, когда взрослые думают, что праздник уже закончен.
So they were just about to continue on their way, but stopped: they looked at the clock and realized it was late. They were going to go, but didn't.
Я попытался было придумать что-нибудь, чтобы они свалили быстрее, но они с места не сдвинулись.
Just like in the third sentence, the narrator started to make up some kind of story to make his opponents leave — but it didn't work.
It is also worth mentioning that in all these examples, you can get rid of "было" and the meaning wouldn't really change.
You can simply say "Я попытался придумать что-нибудь, чтобы они свалили быстрее, но они с места не сдвинулись" — here, "но" and the subsequent explanation are enough to understand that his actions were in vain. But "было" makes the sentence more lively, adds a shade of regret and disappointment, I'd say.
Read more here: https://ru.wiktionary.org/wiki/%D0%B1%D1%8B%D0%BB%D0%BE