The cheapest option is through Cacciola which goes from the boat from Tigre to Caramelo and then a bus from Caramelo to Montevideo... its about half the price of buque but obviously a longer journey...
You can check the rates for the "puente aereo". This air-bridge is similar to others between large cities such as Miami-Orlando, Washington-New York, etc. There are several daily flights at roughly every hour or so. At some points in time, the air-fare can be comparable to Buquebus, and now may be the case, since the blockage of the bridges for car traffic means B-Bus is a monopoly on ground transportation.
Pluna is the small Uruguayian line but it has good planes and service. Also Aero-Vip may still be around with 20-seater commuter planes like some I took from Long Island to Wash DC, and also to Florida. They are cramped and noisy, sort of like a flying "colectivo" but at least they have air-conditioning!!!
Since the flight is only 20-30min, it may pay off for you, even at a slightly higher rate. (The Carmelo trip is several hours) Even with a possible airline strike, I think these smaller Uruguayan carriers still work OK, you can ask this when you inquire.
In case you need tips on locations, in the Capital, my favorite views and walks are mainly around the river´s edge known as "La Rambla" meaning the Avenue boardering the city at the river side.
But time is better spent at Punta del Este, especially now thru April. I would spend the better part of the week over there, and the first and last days in Montevideo.
The city has not been upgraded over the decades, most likely because Punta is only an hour´s drive away, and so that´s where locals invest in week-end and summer houses.