score:8
This should be fine. A few extra days for a bus trip "adventure" is perfectly reasonable, and it's acceptable for a business visitor to engage in "pleasure" activities during the visit.
Now, if the consular officer asks me about my purpose of visit, should I just say "attending a conference", or "attending a conference + sightseeing".
It probably depends on the officer's manner. If the officer is very officious, I would likely just say "attending a conference." But I wouldn't hesitate to add "and doing some sightseeing" if the officer is more receptive.
Also, if s/he asks me why I'd be staying for 10 days, I want to genuinely answer that "I want to do some sightseeing as well" (and go through my above schedule if needed), but is this a "good enough reason"?
Yes.
I don't want my visa to be rejected on the grounds of "unclear purpose of travel".
That seems unlikely. Your explanation here is perfectly clear. You might want to try coming up with concise ways of expressing your goals quickly, in case the officer tends to cut your answers short. For example, instead of "I've decided to travel by bus (since this will be my first visit to the US and I really want to explore it by land)" you could say "I want to take the bus to explore a bit."
Upvote:4
Your primary purpose is to attend the conference. Tell the consular you are going for a conference and planning to stay a couple of days for sightseeing. That's what I told the immigration officer at the airport on my last trip. Of course, he was more interested in the conference.
Upvote:5
Just tell the truth.
You have nothing to hide, you're doing nothing wrong. Your purpose for travel is crystal clear: you're attending the conference and doing a bit of tourist stuff, too. That's completely normal. I like to see a bit of the place if I have to travel half-way around the world, too.