Easy: Just take "Tram 6" (every 6 minutes) directly outside Airport to Bremen Hauptbahnhof.
It takes 16 minutes to your final destination.
from Hamburg Airport: by train
1) Take S-train to Hamburg central station / train will leave each half an hour.
2) At Hamburg central station you change only once to next departing regional train to Bremen central station. Options every half an hour.
Overall riding time: 1h30 to 1h45.
For planning go to http://www.bahn.de and use "Hamburg Airport" as starting point (left box) and "Bremen HBF" as destination (right box).
site in english, go to https://www.bahn.com/en/view/index.shtml
from Hamburg Airport: by bus
Most common is FlixBus / coloured in green.
Website: http://www.flixbus.de, in top Right Corner you can choose your preferred language
As far as I can see/read, information like valid time tables and proper tariffs about "bus travel" f.e. from Hamburg to Bremen with FlixBus are available 6 to 4 weeks before event…
but to get common with search engine just enter f.e. Friday 1st of March as travel date. Website will pop up with some nice rates between 3 Euro and 10 Euro.
Just use some filters on the left side to see what happen:
When you check direct trip and mark Hamburg Airport as departure (bus stops) your travel time jumps up to 2h45. Riding by bus from Hamburg (central station) takes you only 1h30 instead.
from Hannover Airport: by train
1) Take S-train to Hannover central station / train will leave each half an hour.
2) At Hannover central station you change only once to next departing regional train to Bremen central station. Options every half an hour.
Overall travel time: 1h40 to 2h00.
For planning go to http://www.bahn.de and enter "Hannover Flughafen" in left field named "von" which means "from" / and place "Bremen HBF" in right clear box named "nach" which means "to".
site in english, go to https://www.bahn.com/en/view/index.shtml
Costs: by train from Hamburg or Hannover
cheapest option: NIEDERSACHSENTICKET
Validation and costs in general:
Niedersachsenticket is valid from 1 to 5 persons.
1 person pays 24 Euros as a single person travelling.
But when you travel as a maximum group of 5, you pay for each added traveller 5 Euro more.
Which means: 24 + 5 + 5 + 5 + 5 = 44 Euros, so only 8,80 Euro per person.
But it will be still only 1 ticket to purchase, you just choose how many people are with you, and this will be mentioned at ticket printout .
Ticket holder is king!
all others have to follow 
So of course it needs to be the same train connection. 
The more you gather around you, the cheaper you travel.
Restrictions:
You cannot use ICE/IC trains (running a bit faster).
You can only use RB / RE / S trains and trams (in Bremen and Hamburg f.e.), 2nd class only.
But you are free to use your best way/Connection for that day. No reservation needed.
Niedersachsenticket is valid Monday til Friday from 9 am. Saturday and Sunday no limitation.
Where to buy?
You can buy this ticket directly at ticket machines in train stations like Bremen Hbf.
You don´t need to order in advance, but you can do if you like and if you are able to read and understand german: http://www.niedersachsenticket.de
...Just in case you are totally lost right now.
..If you know in advance who will travel with you and you know your plane arrival and departure dates, we can organize that you pay us and we pay the online agency at "Niedersachsenticket.de" (via paypal f.e.) and send your (group) ticket as pdf to your email account including travel options like this: https://www.niedersachsentarif.de/fahrp ... Sel=arrive
We hope we can make your trip as much as enjoyable!
Have a convenient travel time and arrive safe and sound.
