for a travel time of 35 years, you'd not get very long at Proxima Centauri, because you'd still be doing 0.12c when you arrived
The problem, of course, that with a Bussard ramjet, you won't be able to achieve nearly as much acceleration.
edit: according to https://rechneronline.de/g-acceleration/orbital-speed.php, if I got my numbers right (0.12 x solar mass star, .12c = 36000 km/s), the orbit radius would be 1230 km, so you'd be almost at the core of the star since its radius is ~ 100 000 km.