I used to use Blue Host for Wordpress hosting and they were very good at providing everything I needed for that including domain name registration and the like. So I can see why you'd want to only have to deal with one hosting service.
It looks like you're going to have to spend at least $20 a month at Blue Host. So if you only need $10 Digital Ocean plan then are you prepared to pay the difference just to have one hosting account. At $20 and above it is worth trialling both services to see how they perform. Hopefully someone with real knowledge of the two services will post to help you.
On paper with the promotional pricing you seem to get quite a lot at Blue Host. But if you are risk averse, then I'd see Digital Ocean as a much less risky option:
- You know Discourse runs there.
- There are many other Discourse sites using Digital Ocean and I'm not sure if any use Blue Host.
- If there is a bad problem and you have to shift to another hosting service you only pay a month ahead at Digital Ocean versus a year (or more) at Blue Host.
You should also be aware that the Blue Host renewal prices are normally a lot higher. So if you only sign up for one year then the renewal price hits you a lot earlier, e.g. their chart says the Cloud Business Pro account has a three year promotion price of $15.95 but the renewal price is probably the $25.99 they show. Then, if you only take a one year commitment the renewal price will be even higher again. But you probably won't have to pay that because before you have to renew Blue Host is likely to offer you a promotional price to renew with them.