Python simple parser using tags
Python has a style guide, PEP8. I recommend that you follow it, as it makes your code easier to read.
In this case it's mostly just using snake_case, rather than camelCase.
You should use with to automatically close the file. This happens in any circumstance.
Rather than using if startTag in bearFile, I'd invert the if and continue.
Rather than using while you can use for still. This, IMO, is easier to understand too.
You could use a generator function so you don't have to write as much.


Along with a couple of name edits, here's how I'd change your code:

def parse(path, start, end):
    with open(path) as file:
        for line in file:
            if start not in line:
                continue

            for line in file:
                if end in line:
                    break
                yield line.strip()


print(list(parse("bears.txt", "==start==", "==end==")))




To address your concerns:


Do this out of the function. If you ever do want these empty values, then you'll be duplicating code. You also only need to use: 

[item for item in parse(...) if item]

You could implement a function, split_delim, that splits on a delimiter. If you make the function simple, then all you'd need to do is add one line to your function:

def parse(path, start, end):
    with open(path) as file:
        file = split_delim(file, '\n')
        for line in file:
            ...

My changes should remove this error, due to how Python's for loops work. However I havn't tested this.