Now, a couple of observations/questions:
1. Where are you flying in from, and have you ever been to India before?
--If you are jetlagged and landing in the country where all things are possible (and happen instantly before your eyes), it can be a little overwhelming, to say the least. It's therefore very ambitious to try to view sights in Delhi in such condition. It surely can be done, and I admire your bravery! When I get there, I just hole up in my neighborhood for a day and try to re-enter the total insanity I love so much.
If you are going to do something in Delhi, I would recommend the Lal Kila, or red Fort, itself a half-day excursion, followed by the Jamma Masjid, a beautiful mosque built by Shah Jahan (the taj mahal guy). By then probably you will be hungry and deathly tired and will want nothing more than to eat and sleep.
2. The trip to Agra can be about 4 hours by private car, but buses are more unreliable, as they try to fill themselves up by stopping at different places and picking up passengers. I would definitely recommend hiring a private car for the whole time you are there if you can, that way you can make better time.
--A note on India, and Indian roads: NOTHING, I mean nothing runs on time at all. ever. There are so many intangibles and accidents, pedestrians and festivals, roadside dhabas and flat tires that one needs just roll with the changes.
The road to Agra from Delhi is about the best road in India, from there things change. Flyovers are not finished, so massive traffic has to be diverted through smaller towns, there are even places where the road is so pot-holed, you will not believe that it is even supposed to be a road. The road (Even the National Highway) is shared with big trucks, bicycles, strange 3 wheel contraptions (rickshaws and strange "un-rickshaws"), ox carts, pedestrians, and, during harvest season is used to thresh grain by the village people. Overturned trucks and cars are commonplace. Debris on the roads is everywhere, and that's just on the "Highways!!" Your planned journey leads over many secondary roads, and distances can be deceiving. Sometimes you may average 15 or 20 kilometers in one hour. . . Secondary roads are often more dirt than tarmac, and lead through many small villages, some of which your driver may want to stop to make pooja at a temple, buy a cigarette or some guthka, or any number of diversions. He might even want to stop to toss back a quick beer!
Or maybe you will want to do the same. The agra/mandawa/bikaner stretch is mostly these secondary roads, so you never can tell what will happen.
I do know that the Amritsar (eat at the Golden Temple "Langar" when there, it will be worth it) to Dharamsala is a fair hike, you have to cross all of Panjab on mostly secondary roads, and then from Pathankot, up a winding mountain road ( I assume you want to go to McLeodGanj, where the dalai lama lives, and not the actual town of Dharamsala, which is a regular Indian town), so should take some time.
On paper, the distances seem not so far, but in actual practice, we are dealing with India, where everything can happen and definitely does, every day. I would take the estimates and double them, that way you will be pleasantly surprised rather than disappointed. The things you see will be amazing along the way, and alone will be worth the trip.
I would rate this trip at one month, I hope you have that long! Call the boss and tell him/her you will be out longer than expected. . .
The diverse nature of the places you plan to visit bear more in-depth examination for sure!!!
Enjoy yourself, and use an attitude of acceptance rather than irritation when situations arise, live in the moment, and you will do more than you ever dreamed! If you love Mother India, she will love you back.
feel free to pm me if you have anything I can help with.