Hi there, welcome to the forum!
So you have two options, either a government-operated bus or a private bus for reaching Delhi from Jaipur. The government buses are operated by the Rajasthan State Road Transport Corporation (RSRTC). There are some RSRTC Volvo buses that depart early from Jaipur. Here are their timings, along with the express buses:
Early Morning Buses from Jaipur to Delhi (RSRTC)
| Bus Type and Number | Departure Time | Arrival Time |
| Express Bus No. 1 | 4:05 | 9:30 |
| Express Bus No. 2 | 4:25 | 10:00 |
| Express Bus No. 3 | 4:40 | 10:20 |
| Express Bus No. 4 | 4:50 | 10:40 |
| Express Bus No. 5 | 4:55 | 11:00 |
| Volvo Mercedes No. 1 | 5:00 | 11:00 |
| Express Bus No. 6 | 5:05 | 11:05 |
| Express Bus No. 7 | 5:10 | 11:20 |
| Express Bus No. 8 | 5:15 | 11:25 |
| Express Bus No. 9 | 5:18 | 11:30 |
| Express Bus No. 10 | 5:45 | 11:50 |
| Volvo Mercedes No. 2 | 6:00 | 12:00 |
With the RSRTC, there are only two Volvo buses departing early in the morning from Jaipur to Delhi. The first one departs at 4:55 and the second one departs at 6:00. So if you'd like to board any of these buses, you have to alter your schedule and leave a bit later than you have planned. Journey duration is around 5 to 6 hours. Fare would be around Rs. 450 to Rs. 650, depending on which type of bus you board. If you really have to leave that early, there are plenty of RSRTC express buses departing as early as 4:05 from Jaipur. These buses depart from Sawai Ram Singh Road in Jaipur.
With regards to the private buses, there are also plenty of them operated by different companies. Here are some private buses plying this route, starting from 3:45 am, since that is the time you said that you're leaving from Jaipur:
Early Morning Buses from Jaipur to Delhi (Private)
| Bus Company (Bus Type) | Departure Station - Time | Arrival Time | Fare |
| Shrinath Travel and Transport Agency (Multi-Axle Volvo Bus) | Near Krishna Dharm Kanta - 3:45 | 9:30 | Rs. 3,548 |
| Shrinath Travel and Transport Agency (AC Sleeper Bus) | Near Krishna Dharm Kanta - 4:15 | 9:15 | Rs. 812 |
| Shrinath Travel and Transport Agency (Tata AC Sleeper Bus) | Near Krishna Dharm Kanta - 5:05 | 10:05 | Rs. 3,000 |
| Goldline Super Deluxe (Tata Non AC Bus) | Opposite Shantosh Bhojnalaya Shindhi Camp - 6:40 | 12:40 | Rs. 250 |
As you can see, only two private bus companies have schedules around 4:00 am. Shrinath Travel and Transport Agency has the most number of buses plying during this time but the rates are incredibly expensive. If you are okay with an AC Sleeper bus, it is more affordable than the Volvo bus or the Tata AC bus. Journey duration is around 5 hours.
I hope this helps you.
