As a general rule the more letters of RETAINS you have, the greater the chance of a bonus. 

Below are all the bonus words you can make if you have six of those letters, ASTERN, and one other letter.

There are a lot of words, so to make learning easier, perhaps break them down into groups of 10-15 words or by distinct letter groups (i.e ANTERS+A, B, C, D and E).

ASTERN + 

A - ANESTRA, SANTERA

B - BANTERS, BARNETS

C - CANTERS, CARNETS, NECTARS, RECANTS, SCANTER, TANRECS, TRANCES

D - DARNEST, ENDARTS, STANDER, STARNED

E - EARNEST, EASTERN, NEAREST, RATEENS, STERANE

F - nothing

G - ARGENTS, GARNETS, STRANGE

H - ANTHERS, HARTENS, THENARS

I - ANESTRI, ANTSIER, NASTIER, RATINES, RESIANT, RETAINS, RETINAS, RETSINA, STAINER, STARNIE, STEARIN

J - nothing

K - RANKEST, STARKEN, TANKERS

L - ANTLERS, RENTALS, SALTERN, SLANTER, STERNAL

M - ARTSMEN, MARTENS, SARMENT, SMARTEN

N-  TANNERS

O - ATONERS, SANTERO, SENATOR, TREASON

P - ARPENTS, ENTRAPS, PANTERS, PARENTS, PASTERN, PERSANT, TREPANS

Q - nothing

R - ERRANTS, RANTERS

S - SARSNET, TRANSES

T - NATTERS, RATTENS

U - AUNTERS, NATURES, SAUNTER

V - SERVANT, TAVERNS, VERSANT

W - STRAWEN, WANTERS

X - nothing

Y - TRAYNES

Z - nothing

76 words in total. 5 letters ASTERN doesn't combine with to make a bonus (F, J, Q, X and Z).