Alternatively, don't kill the host but make her (also him, but less important) infertile.
Because this:
The most dangerous disease has long-ass latency.
We'll assume that you're able to make a designer disease which can proliferate amongst hosts, render them infertile and have few other symptoms.
The biggest problem with that weapon is when it inevitably gets back to you.
We'll go with the most obvious, first- Say the enemy knows that you're the one who dropped this fuckoff bomb on them. First thing they're going to do is go to war with you. Now, it doesn't matter if you're invading them or they're invading you, either way their infected soliders are going to be 'interacting' with your infected soldiers. You'd be surprised how many diseases have managed to cross no-man's land in the past.
Secondly, bioweapons, like Neutron bombs, are designed to be 'discriminate killers'. That is- they kill a lot of humans and leave a lot of infrastructure behind- so that when you invade/colonize, you've got barracks for your men and crops for your farmers, all waiting to go.
First issue there- you're going to have a city full of people, who may not yet realize that they're sterile.
Which is fine, you don't have to take over that settlement, you can just wait out the generations and hope that this new disease doesn't cross to your country.
But just in case you managed to push them out/win the war, you've now got a country filled with sterile PoW's and civilians, who still might be infectious- again causing issues for your own country.
A standard bioweapon would be more useful in a terror attack, too.
... Yes I have thought way too much about this.
A Chinese Officer here once on exchange produced the standard line about how the Chinese could lose 500 million people in a nuclear war and keep going with the survivors. So his hosts got out a demographic map (one that shows population densities rather than topographical data) and got to work with pie-cutters using a few classified tricks - and got virtually the entire population of China using only a small proportion of the US arsenal. The guest stared at the map for a couple of minutes then went and tossed his cookies into the toilet bowl.
Holy Crap.