Once you have arrived in Managua you have two main options for traveling from the city to Bluefields.
Option 1 – Flying
You can purchase tickets to fly to Bluefields from Managua directly at the Managua airport. La Costeña Airlines is the most popular for domestic flights within Nicaragua, and they also offer flights to nearby countries. You can view schedules and fares by visiting the La Costeña Airlines web-site. Flights cost about USD $130, with three fights leaving in the morning (two early and one mid-morning) and one flight leaving in the early afternoon. Currently the online booking section of the La Costeña Airlines web-site is under construction, so in order to make inquiries regarding reservations online the site suggests you email reservacion@lacostena.com.ni. The flight is around an hour, and one round-trip ticket secures you 50 lbs of stowed luggage and a carry-on bag.
Option 2 – Bus and Boat
The bus and boat method is for those whose travel is dictated by money, not by time. This method is by far the more economical, but it also takes 10 times the amount of time. The entire trip from Managua to Bluefields by bus and boat takes roughly between 10 and 12 hours, but costs a fraction of flying there, at about USD $20 for the entire trip.
The tried and true way is by taking an overnight bus from Managua to he port city of El Rama, where you catch the boat that goes down the river to Bluefields. If you prefer a more comfortable 10 hour drive to the Atlantic Coast you can contract a private bus 
company such as Empresa Vargas Peña (tel 280-1812 in Managua; tel 822-1410 in Bluefields) who provide service from Managua to El Rama, and then a connection to the boat that takes you to Bluefields. Empresa Vargas Peña departs three times daily from the Mercado Iván Montenegro in Managua: 5 am, putting you in Bluefields at 3 pm, a 2:45 pm departure, staying overnight in El Rama and completing the boat leg in the morning, and a 9:30 pm departure, arriving in Bluefields at 7:30 am the following day.
Bluefields may not be the easiest place to get to in Nicaragua, but it is worth the work.
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Your site is very informative. Thank you very much. I really appreciate it.
Elisa
Thanks for these tips, they are great. The number for Vargas Pena in Managua has changed, though. It is now 2253-2879.
What kind of plane is it. Is it a 6 seater small plane that La Costeno uses between Managua and Bluefields?