It is common for English speakers to say either 'better' or 'best' in this context. However, the grammar rule is based on the 3 different forms that an adjective can take, namely, "good, better, best". Tim is right to say, "The speaker is implying that there are 2 options: to ask or not to ask." When the adjective is comparing 2 things (nouns) then the Comparative form of the adjective should be used, hence "better". If one used "best", then there would have to be more than 2 options or choices or subjects that are being compared. So, the proper, grammatically correct adjective form is "better". But people are lazy, in every language, and they often don't follow the exact grammar rules. "Best" has one syllable, and "better" has 2 syllables. Even though it's not that much more difficult to pronounce 2 syllables, many people will choose to use the shorter one syllable word.

You can use either word in this context. The speaker is implying that there are 2 options: to ask or not to ask. When there are only 2 options the better option is also the best option.