The classic answer to this question is a coffee shop. There are a couple of Starbucks locations nearby that open at 5:30am (on weekdays, check the hours on weekends), including one very close by on 7th just before 28th St. You could grab a drink, perhaps a bite to eat, and hang out for a couple of hours. Non-Starbucks options are available and recommended too, including Stumptown at 29th and Broadway (opens at 6am weekdays). If the weather is nice, you could wander over to Madison Square Park or (if you don't have a lot of luggage, as it's somewhat farther away), the High Line (opens at 7), or even walk up to Times Square if you've never seen it, and explore by yourself for a bit.
It's hard to recommend sightseeing since you don't have much time and we don't know what you like to do. Do you have any particular interests? Unfortunately, most museums aren't really a practical option, as many don't open until 10am or later, which would leave you with very limited time. You could consider a delicious brunch.
It's absurdly expensive ($100) and I've never done it, but I'll mention only since you're in just the right time and place (if your bus is on time), it's now possible to see the sunrise from the Empire State Building.