The most common and most likely answer to this crossword clue is the 3 plus 7 letter word RUN LENGTHS
R
U
N
L
E
N
G
T
H
S
Buddy explains!
The straight part
We know that "Series of bi-singles" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case series of bi-singles = run lengths.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.