Issues optimizing postgres search query

I am having an issue with the following PostgreSQL query it takes more than 10 seconds to run is there any way to speed this query up to a rational speed, I am simply looking for the most relevant search terms associated with videos on a very large database.

  SELECT count(*), videoid 
  FROM term_search 
  where word = 'tester' 
     OR word = 'question' 
     OR word = 'one' 
  group by videoid 
  order by count(*) desc 
  limit 1800;

When the query is run with analyze the resultant query plan is as follows (http://explain.depesz.com/s/yDJ):

  Limit  (cost=389625.50..389630.00 rows=1800 width=4) (actual time=11766.693..11770.001 rows=1800 loops=1)
     Output: (count(*)), videoid
     ->  Sort  (cost=389625.50..389692.68 rows=26873 width=4) (actual time=11766.689..11767.818 rows=1800 loops=1)
           Output: (count(*)), videoid
           Sort Key: (count(*))
           Sort Method: top-N heapsort  Memory: 181kB
           ->  HashAggregate  (cost=387769.41..388038.14 rows=26873 width=4) (actual time=9215.653..10641.993 rows=1632578 loops=1)
                 Output: count(*), videoid
                 ->  Bitmap Heap Scan on public.term_search  (cost=44915.83..378163.38 rows=1921207 width=4) (actual time=312.449..7026.036 rows=2047691 loops=1)
                       Output: id, videoid, word, termindex, weight
                       Recheck Cond: (((term_search.word)::text = 'tester'::text) OR ((term_search.word)::text = 'question'::text) OR ((term_search.word)::text = 'one'::text))
                       Rows Removed by Index Recheck: 25512434
                       ->  BitmapOr  (cost=44915.83..44915.83 rows=1950031 width=0) (actual time=288.937..288.937 rows=0 loops=1)
                             ->  Bitmap Index Scan on terms_word_idx  (cost=0.00..8552.83 rows=383502 width=0) (actual time=89.266..89.266 rows=419750 loops=1)
                                   Index Cond: ((term_search.word)::text = 'tester'::text)
                             ->  Bitmap Index Scan on terms_word_idx  (cost=0.00..13171.84 rows=590836 width=0) (actual time=89.700..89.700 rows=604348 loops=1)
                                   Index Cond: ((term_search.word)::text = 'question'::text)
                             ->  Bitmap Index Scan on terms_word_idx  (cost=0.00..21750.26 rows=975693 width=0) (actual time=109.964..109.964 rows=1023593 loops=1)
                                   Index Cond: ((term_search.word)::text = 'one'::text)

The schema for the table is as follows:

    Column   |          Type          |                        Modifiers                         | Storage  | Description 
  -----------+------------------------+----------------------------------------------------------+----------+-------------
   id        | integer                | not null default nextval('term_search_id_seq'::regclass) | plain    | 
   videoid   | integer                |                                                          | plain    | 
   word      | character varying(100) |                                                          | extended | 
   termindex | character varying(15)  |                                                          | extended | 
   weight    | smallint               |                                                          | plain    | 
  Indexes:
      "term_search_pkey" PRIMARY KEY, btree (id)
      "search_term_exists_idx" btree (videoid, word)
      "terms_caverphone_idx" btree (termindex)
      "terms_video_idx" btree (videoid)
      "terms_word_idx" btree (word, videoid)
  Foreign-key constraints:
      "term_search_videoid_fkey" FOREIGN KEY (videoid) REFERENCES videos(id) ON DELETE CASCADE
  Has OIDs: no

I have managed to get it down to 7 seconds with Index Only scans but it was still not low enough. I am running PostgreSQL 9.3 on Ubuntu 14.04 on an aws r3.xlarge instance, with approx 50 million rows in the table. Any advice is greatly appreciated!

EDIT:

Attached is the result of SELECT schemaname,tablename,attname,null_frac,avg_width,n_distinct FROM pg_stats WHERE schemaname='public' and tablename='term_search';

 schemaname |  tablename  |  attname  | null_frac | avg_width | n_distinct 
 ------------+-------------+-----------+-----------+-----------+------------
 public     | term_search | id        |         0 |         4 |         -1
 public     | term_search | videoid   |         0 |         4 |     568632
 public     | term_search | word      |         0 |         6 |       5054
 public     | term_search | termindex |         0 |        11 |       2485
 public     | term_search | weight    |         0 |         2 |          3

Solution

If I have a chance to disconnect users for a night I would:

create a new table with words from term_search,
create reference to the new table,
drop column word,

something like this:

create table words (
    word_id serial primary key,
    word text);

insert into words (word)
    select distinct word
    from term_search;

alter table term_search add column word_id integer;

update term_search t
    set word_id = w.word_id
    from words w
    where t.word = w.word;

alter table term_search add constraint term_search_word_fkey 
    foreign key (word_id) references words (word_id);

Test:

SELECT count(*), videoid 
FROM term_search t
JOIN words w on t.word_id = w.word_id
WHERE w.word = 'tester' 
   OR w.word = 'question' 
   OR w.word = 'one' 
GROUP BY videoid 
ORDER BY count(*) desc 
LIMIT 1800;    

-- if was faster then
    alter table term_search drop column word;
-- and on the fly...
    alter table term_search alter termindex type text;

After the revolution I'd have to take care of inserts and updates on term_search. I'd probably create a view with rules for insert and update.