Does China have long range bombers at this time that can reach the
continental United States?

China has Tu-16 bombers which might be able to reach Alaska and maybe parts
of the US west coast on a suicide (read, one-way) mission.
They are rumoured to have at least a few Tu-22M (Tu-26) Backfires as well
which could reach the US west coast.

Although they have nuclear bombs, what about the planes to deliver
them?

Certainly.
Not to mention ICBMs which can reach parts of the US and several (at least
1, possibly 3 or more) SSBNs with 8+ MIRVed SLBMs each.

I know China had some TU-16 planes years ago, but did they ever
develop long range bombers or get any from the former Soviet Union?

Tu-16 both from the USSR and built by themselves. I guess they've improved
on them for better range by now to reach the US.
They can certainly reach Moscow...

And what about China's in-air refueling capability?
Limited.

China is not much of a nuclear threat to CONUS, but the northwest is at risk
as are forces in theater (Korea, Japan, Philipines, Thailand, Malaysia,
Singapore, etc.).

Draw a circle centered on central China and reaching to Moscow and you have
the range (approximately) where the PRC can project their nuclear weapons
to.