Thinking about running the following list for NOVA next month:

Durin
12 Hearthguard
3 Vault Warden Teams

Kings Champion & Heralds
5 Dwarf Warriors w/ Shield
4 Dwarf Warriors w/ Bows

Captain w/ Shield
8 Iron Guard

40 models, 7 might

Alternatively:

Durin
18 Hearthguard

Kings Champion & Heralds
3 Vault Warden Teams
2 Dwarf Warriors with Shields
2 Dwarf Warriors with Bows

Captain w/Shield
6 Iron Guard

39 Models, 7 Might

I'd go second list all the way. In essence you're upgrading 6 dwarves to Hearthguard for the price of 2 iron guard. That seems like a great trade to me.

Should I even bother with the bows? Or just take warriors with shields?

For this list I wouldn’t bother with the bows. Not enough to make them worth it in my opinion.

I don't know which scenarios are being run at NOVA this year but I would recommend replacing all the shields in the second list with bows. The main fighting force has no range and will be in trouble against things with magic or good range but, as the Texan said, a few 18'in bows wont help that much. I do think they would be better guards for rear objectives or a camp if they had bows to threaten anything running back later in the game. Shields can wait for something to reach them and then shield to hold off larger groups its true, however, the objective will still be contested and horsemen will still come in mounted. Bows could stave things off and keep the objective under your control. Definitely go with the shields if you are not planing to use them for objectives though.

_________________
"Draw your sword with a heavy heart, but swing it with a heavy hand"

It's been ages, since I played Khazad-Dum and I haven't played it with the new edition yet, so probably my opinion is not the most professional one, but I'd go with the first list.
Hearthguard is great, but I think scenario-wise, it's alwyas useful to have something in every company that can either shieldblock or stand their ground (like the Vault Warden Team). Plus, I'm a huge fan of dwarven archery, they're always so much better than you'd expect from dwarves. Eventhough they don't have great range, their 4+ and S3 is still some kind of thread in a bunch of 4 or 5 and produce an area denial for small groups of low Ds and Kav that sneak around trying to capture outer control points. You will be defenitly too slow, to catch up with them, attacking them in close combat.
I'd swap some of the troops around the companies though, especially dwarfs don't merge as well during the game due to their limited movement. E.g. maybe one of the Warden Teams to another group. There's always a strategically important but narrow zone, that can be easily blocked by a single Warden Team.

Maybe I blend the two:

Durin
16 Hearthguard
1 Vault Warden Team

Kings Champion & Heralds
1 Vault Warden Team
4 Warriors w/ shields
4 warriors w/ bows

Captain w/ shield
1 Vault Warden team
2 Warriors w/ Shields
4 Iron Guard

OR

Durin
16 Hearthguard
1 Vault Warden Team

Kings Champion & Heralds
1 Vault Warden Team
6 warriors w/ bows

Captain w/ shield
1 Vault Warden team
4 Warriors w/ Shields
4 Iron Guard

I advocate against splitting up the wardens. There are too few spaces small enough for a single team to hold on NOVA maps for it to be worth it and you'd get much better results out of having them together to cut off larger areas or form the center of your line.

_________________
"Draw your sword with a heavy heart, but swing it with a heavy hand"