Gosh, just the thought of staying in a tent in DR, no matter how supposedly glamorous it is. No A/C, no toilet, things crawling over you all night. Not for this lady.
Back to the OP's question, I would strongly suggest that you maybe think about giving up a night in the delightful tent go to Barahona the previous day and stay in a little hotel. If not I suspect you will need to transit in the dark, which won't be fun, or worse the transfer won't appear and you will end up missing your bus (and I suspect then missing a flight). Things in DR very often don't go to plan, it's hard to find reliable people who will turn up, especially super early.
By the way, when negotiating a fare, bear in mind that the poor person who takes you then needs to make the same journey back. Fuel is more expensive here than in the US, and just look around at the poverty. Not sure if you really need to try to screw someone down to US$ 15 for a 4-5 hour drive. Have a little compassion.