Steven Roby & Brad Schreiber described a the Bonnevilles recording session in Becoming Jimi Hendrix. There is no known date for the session and the recordings are not in circulation so this information remains unconfirmed:

August-November? 1963 with the Bonnevilles
Fidelity Recording, Nashville, Tennessee
The Bonnevilles recording session with Robert Fisher - keyboards, Jimi Hendrix - lead guitar, Larry Lee - rhythm guitar, Unknown - bass, Isaac MacKay - drums, Harrison Callaway - trumpet and Aaron "Heinz Ketschup" Varnell - saxophone. The band records "Snuff Dripper", "Ouch" and two more numbers. 1

What is confirmed is that Jimi did tour with the Bonnevilles. He sent postcards to his father but these do not mention the artists(s) that he was traveling with. The date of the second and locations mentioned in it are however a match with a gig advert for the Bonnevilles published in the Miami Herald on 9 October 1964. So the postcards and the ad together give us approximate dates and locations for some of the gigs that Jimi played with the band:

Sunday? 27? September 1964 with the Bonnevilles
Columbus, Ohio

Postcard to Al Hendrix, stamped Monday 28 September 1964 in Columbus, Ohio
(Postcard depicts Port Columbus airport):
" Dear Dad. I hope everything's fine. Well here I am again, traveling to diffrent places. I'm on a tour which lasts about 35 days we're about 1/2 through it now. We've been through all the cities in the midwest east & south I'll write soon Jimmy" 2

Postcard to Al Hendrix, stamped Thursday 8 October 1964 in Cincinnati, Ohio

(Postcard depicts the skyline of Jacksonville, Florida):
" Dear Dad. Here we are in Florida, we're going to play in Tampa tomorrow - then Miami, we're playing all through the south. We'll end up in Dallas Texas. My home address is Atlanta. I hope everyone's ok tell Grama in Canada hi for me. Tell Leon to be kool and go to school. I must run now - take it easy - My address is 318 Fort St. APT. 3 Atlanta Ga. Jimmy" 2

Thursday? 8? October 1964 with the Bonnevilles
Tampa, Florida

Friday 9 October 1964 with the Bonnevilles
Jet Lounge, Miami, Florida

09 Oct 1964, Fri The Miami Herald (Miami, Florida)
? October 1964 with the Bonnevilles
Dallas, Texas

1 Information about the session comes from the book "Becoming Jimi Hendrix" by Steven Roby & Brad Schreiber. The authors quote no source for the information given as part of the "Sessionography" (page 201) but the "Acknowledgements" (page vii) thank Robert Fisher for "interviews and valuable time" so one would assume he is the source. There is a typo in the "Sessionography" with Isaac MacKay spelled as "Issac".

2 Reproduced in the book "Jimi Hendrix A Visual Documentary" by Tony Brown.