Looking back through the thread, I see Bluehost wants you to use the Partner setup, so DNS is set at Bluehost.
That last screen does show a proper A record for your main domain, denoted by the @. The MX record also looks good. If possible, can you change the TTL to 300 on everything? That way, any changes take effect in about 5 minutes, rather than 4 hours (14,400 seconds).
Focusing just on your website, Bluehost says all you need to do is “Activate” Cloudflare in the Domains section. I’d change the TTL, then wait 4 hours for all DNS to update, then Activate your domain for Cloudflare.
If it’s still broken, start bugging Bluehost relentlessly.
(Read next post for how I handle Cloudflare setups)
EDITED: Changed TTL to 300 seconds (5 minutes) instead of 3600 seconds (1 hour).