I thought about possible routes to complete the "Big Game Mode" as fast as possible and came up with these two ways.

Pick Cydney as character, since she has the women speed bonus on some bikes and the most starting cash ($1000). Note you always get additionaly half the value of your current bike when you buy a new one.

First, win 3 races (+ $3000) so you will have a total of ($5748) available and buy the "Rat" (- $5489 = $259). Then..

Route A

• Win next 7 races (rest of lv1 and all lv2 races = +$12000) and buy the "Vampiro" ($15003 - $13796 = $1207)
• Win next 8 races (lv3 and three lv4 races = +$27000) and buy the "Assassino" ($35105 - $34888 = $217)
• Win next 5 races (rest lv4 and three lv5 = +$23000) and buy "Vipera" ($40661 - $40000 = $661) and finish final 2 races

Route B

• Win next 9 races (lv1, lv2 and two lv3 races = +$18000) and buy the "Raven" ($21003 - $18999 = $2004)
• Win next 8 races (lv3 + all lv4 = +$29000) and buy the "Vipera" ($40503 - $40000 = $503) and finish lv5

Its not particularly easy to win a lv3 race with the "Rat" or a lv4 race with a "Vampiro" so one could buy a worse bike than listed as safety strat, but it should equal a significant time loss. Time estimates for both routes were about even in my calculations.

After getting annoyed on failing Sierra Nevada LVL3 , more often than I'd like to admit, i came up with a "backup"

starting off the same here, Win next 7 races (rest of lv1 and all lv2 races = +$12000) and buy the "Vampiro" ($15003 - $13796 = $1207)

After level 3 : (so start lvl 4) i bought 750cc Kamikaze N Also did lvl 5 city with this bike, upgraded to stiletto (900cc Assassino) after.

Finished a run, lots of trouble at Napa Valley lvl5 sadly (and lost like ~14minutes or so there)

Small update; Napa Valley(8km) is the shortest race at lvl 1, so if u start at Sierra Nevada, u can do city with the rat killer, and save a couple off seconds there compared to my run on the board, (make sure u get the upgrade before u start Pacific highway (8.8km) tho) :)