You will never get the bike out the door for $3,800.
You put down whatever you want to put down. You can probably go ZERO down, but your payments will be higher per month. Financing anything is about 3 things:
1. Total cost of the thing you are buying
2. Interest rate
3. Duration of the loan
A "down-payment", or a "trade-in" will affect the value of #1 .
Your "credit rating" will affect the value of #2 .
That "$3,800" bike, will be $5,000 at the bottom of the sales contract. Maybe more. If you put $1,000 down, you finance $4,000.
With an interest rate of 3.0%, and a duration of 48 months, your payment would be $88 per month.
( Don't forget to factor-in Insurance costs, and riding-gear if you don't already have it! )