I doubt if ". . . hate to lose" is the problem.
It's a bad time of the season to try to break into a league, since most league seasons are two months or less from completion.
I'll pass along my two cents, FWIW. I bowl a league at Woodview Lanes (formerly Espo's Country Lanes) in Elgin. It's located on Woodview Drive, just off of Irving Park Road (Chicago St.) on the east side of Elgin, just west of Elgin Toyota. I don't have a phone number handy, but I'm sure you could look them up in the phone book. Although it is probably outdated, they have a sign up as you turn the corner off of Irving Park saying "Bowlers Wanted."
If you don't get in this year, I'd recommend that you consider joining the Friday Night Men's League there next season. It's a reasonably competitive 5-man team league, usually with around 20 teams. The prize money is decent, and there is plenty of side action, such as brackets, survivors, high game pots, doubles pots, etc.
Feel free to PM me if you have any questions.
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RW (THB)