You can take your bike on the train outside rush hours (06:30 - 09:00/16:30 - 18:00) and it will cost you €6 per bike, per day, but don't get your bike in Amsterdam and transfer it to Arnhem, this is just way too much hassle.
According to this website, there are 5 bikeshops where you can rent bikes in (the neighbourhood of) Arnhem. Namely:
Here is a map showing these bikeshops around Arnhem. In this way you can decide which shop you choose based on the region where you want to bike.
I've linked the above names to the rental web page (or contact page if there's no rental page) so you can see the information for yourself. As you don't speak Dutch and the website might be unavailable I've also summarised the information below. Prices are per day, unless otherwise noted. Regular opening hours are 09:00 - 17:00.
Bike's can be delivered and picked up by the company (probably additional costs). On Sunday and Monday they're closed, so no bikes can be rented or returned.
- Mountainbike - €15
- City bike - €7.5, with electrical engine €30
- Kid bike - €5
- Half wheeler - €7.5
- Deposit - €50
It's mandatory that you can show an identification document.
If you choose a mountain bike, keep in mind that you have to return it clean. Otherwise a €10 charge per dirty bike will be incurred.
This company does not have rental information on their website, but you can e-mail them or give them a call to ask for their rates. Closed on Sunday and Monday.
Closed on Monday and Friday open until 20:00.
- Mountainbike - €15
- Three speed city bike - €7.5
- Electrical bike - €22.5
- Tandem bike - €15
- Deposit - €100
It's mandatory to show a valid identification document. If you rent a bike for a week you will only pay 5 days. If you want to rent a bike you can make a reservation by phone (+31 317 31 23 72).
Closed on Mondays unless it's a school holiday. This varies per year so if you want to rent a bike on Monday you should just contact them to ask if they're open.
- Mountainbike 29" wheels - €20
- Mountainbike 26" wheels - €17.5
- Kid mountainbike - €12
- Multispeed City bike - €8.5
- Multispeed Tandem - €18
- Kid bike - €6
- Half wheeler - €6
- Kid tandem - €18 or €10 for a half day