Its pretty common for flights to leave Bali late. Lately, Jakarta airport seems to be responsible for many of these delays as they are still trying to get the new terminal operating smoothly.

Avoid LionAir at all cost, we pretty much call them LateAir.

I can't speak for the air-side bus at T3, that sounds like the way to go.

The intra-terminal bus system is slow, infrequent, and crazy. It's out on the street at arrivals. Last time I tried to transfer, 50 Indonesians jumped ahead of me in line. I couldn't fight much as I had three bags. I gave up and went for a taxi. Another time, it took an hour to get to the terminal I wanted as they stopped at the other terminals, and there's a ton of traffic around too.

Easier is to take a taxi. The non-BlueBird taxis will try and charge you a ton, so bargain hard (I'd walk away from 2-3 and let them chase you for a lower price) or avoid them. There's a Bluebird stop at most terminals and it'd cost less than 20k to get to your terminal. They might give you the evil eye for such a ride but they'll do it, and I'd tip accordingly. Uber works at the airport but the drivers never seem to be able to find you.

If I was going to transit at JKT, I'd build in at least a 5-hour buffer: 2 hours for a late flight, 1 hour to transfer, and the normal 2-hours ahead for an International Flight.

I usually fly in the night before and get a transit hotel near the airport, there's a ton of them listed on Booking.com/Agoda. Then again one of my travel rules is to be in city of my international departure the day before.

There's not much landside at the airport, but there are some nice lounges inside and they don't charge much, so get there early and get into a lounge.

Interestingly, getting from "downtown" Jakarta to the airport might be even more difficult than from Bali. I almost missed my flight once and left from downtown 4 hours early.