Yes, bought is in the scrabble dictionary

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Bought Definition

verb

Past tense and past participle of buy. See Regional Note at boughten.

from The American Heritage Dictionary of the English Language, 4th Edition

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Top Words by points	Points
bought	12

2 letter words with BOUGHT	Points
ho	5
ut	2
uh	5
bo	4
to	2
oh	5
go	3

3 letter words with BOUGHT	Points
out	3
hot	6
hub	8
hug	7
hut	6
hog	7
tho	6
tog	4
tub	5
tug	4
ugh	7
bog	6
bot	5
gut	4
got	4
gob	6
bug	6
but	5
hob	8

4 letter words with BOUGHT	Points
bout	6
thug	8
thou	7
bhut	9
both	9
goth	8
gout	5

5 letter words with BOUGHT	Points
bough	11
ought	9
butoh	10
tough	9

6 letter words with BOUGHT	Points
bought	12

Found 38 words in 0.16427 seconds