better still:

 explain analyze SELECT DISTINCT BugBranch.branch
FROM Bug,
     BugBranch
WHERE BugBranch.branch IN (451217, 451208, 451207, 451206, 310641, 450226, 449792, 449762, 449192, 449190, 444685, 439423, 436128, 421710, 317004, 374978, 404904, 412011,  411115, 245099, 400223, 377965, 373979, 372939, 372691, 362490, 362566, 362564, 361252, 359795, 359423, 357633, 355943, 348553,
322307, 319438, 316198, 316197, 315929, 310090, 308190, 305716, 305524, 296541, 294443, 245102, 275463, 273980, 40682, 34254, 175815, 152799, 115607, 81913, 81670, 62623, 52209, 42949, 39318, 38448, 37654, 12332, 30797, 21766, 13518, 16918, 12486, 10605, 10457, 5670,  9447, 7882, 4233, 3674, 2510, 2469)
  AND Bug.id = BugBranch.bug
  AND (Bug.private = FALSE
       OR exists 
         (SELECT TRUE 
          FROM BugSubscription,
               TeamParticipation
          WHERE TeamParticipation.team = BugSubscription.person
            AND TeamParticipation.person = 67034 and bug.id=BugSubscription.bug));
                                                                                                                                                                                                                                                                                QUERY PLAN                                                                                                                                                                                                                                                                                 
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 HashAggregate  (cost=12527.12..12527.51 rows=39 width=4) (actual time=186.053..186.064 rows=18 loops=1)
   ->  Nested Loop  (cost=0.00..12526.88 rows=97 width=4) (actual time=1.613..186.019 rows=18 loops=1)
         ->  Seq Scan on bugbranch  (cost=0.00..9341.04 rows=97 width=8) (actual time=1.585..185.567 rows=18 loops=1)
               Filter: (branch = ANY ('{451217,451208,451207,451206,310641,450226,449792,449762,449192,449190,444685,439423,436128,421710,317004,374978,404904,412011,411115,245099,400223,377965,373979,372939,372691,362490,362566,362564,361252,359795,359423,357633,355943,348553,322307,319438,316198,316197,315929,310090,308190,305716,305524,296541,294443,245102,275463,273980,40682,34254,175815,152799,115607,81913,81670,62623,52209,42949,39318,38448,37654,12332,30797,21766,13518,16918,12486,10605,10457,5670,9447,7882,4233,3674,2510,2469}'::integer[]))
         ->  Index Scan using bug_pkey on bug  (cost=0.00..32.83 rows=1 width=4) (actual time=0.020..0.020 rows=1 loops=18)
               Index Cond: (bug.id = bugbranch.bug)
               Filter: ((NOT bug.private) OR (alternatives: SubPlan 1 or hashed SubPlan 2))
               SubPlan 1
                 ->  Nested Loop  (cost=0.00..26.48 rows=1 width=0) (never executed)
                       ->  Index Scan using bugsubscription_bug_idx on bugsubscription  (cost=0.00..7.26 rows=3 width=4) (never executed)
                             Index Cond: ($0 = bug)
                       ->  Index Scan using teamparticipation_team_key on teamparticipation  (cost=0.00..6.39 rows=1 width=4) (never executed)
                             Index Cond: ((public.teamparticipation.team = public.bugsubscription.person) AND (public.teamparticipation.person = 67034))
               SubPlan 2
                 ->  Nested Loop  (cost=0.00..2954.48 rows=4062 width=4) (never executed)
                       ->  Index Scan using teamparticipation_person_idx on teamparticipation  (cost=0.00..273.54 rows=106 width=4) (never executed)
                             Index Cond: (person = 67034)
                       ->  Index Scan using bugsubscription_person_idx on bugsubscription  (cost=0.00..25.17 rows=10 width=8) (never executed)
                             Index Cond: (public.bugsubscription.person = public.teamparticipation.team)
 Total runtime: 186.279 ms
(20 rows)