Learn Russian: У меня к вам один вопросик.

Adding the diminutive suffix -ик to вопрос (question) softens the request. The speaker isn't necessarily asking a physically short question; rather, they are being polite and trying not to sound demanding or intrusive. In English, we often achieve this same feeling by saying 'I have a quick question'.

Why do we use к вам instead of для вас when the English translation says 'for you'?

In Russian, questions are directed toward someone, so you use the preposition к (to/toward) plus the dative case (вам). Using для вас (for you) would sound strange here, almost as if you acquired a question on their behalf rather than asking them to answer it.

Does один just mean 'one' here, or is it doing something else?

While it literally means 'one', in conversational Russian it often acts similarly to the English article 'a'. Here, it pairs perfectly with the diminutive вопросик to further minimize the interruption, reassuring the listener that the interaction will only take a brief moment.

Is it appropriate to use вопросик to soften a request in a formal business meeting?

Usually, no. Despite being a softening tool, diminutives like вопросик sound very casual and familiar. In a strictly formal or highly professional setting, it is safer to stick with the standard У меня к вам вопрос, which you might soften instead by using the conditional mood or polite introductory phrases.