As foreigner tourist you can book and pay for bike rental directly from your country. I know more about rental in Royal Brothers company. As foreigner you can not create account there because conformation OTP (One time password) works only with Indian phone numbers, so you must connect this company via email and arrange your bike. Staff is helpful. Here is one trick which you MUST keep in mind - prices on they website doesn't show taxes (*All prices are exclusive of taxes and fuel. Images used for representation purposes only, actual color may vary.), so final price is higher then you will see, for example, here:

Here, in Bengaluru is few more rental companies, but some of them rent only scooters. Serious looking (but only on website) is twistthrottle.in. But I, personally, do not trust them because they ignored mail I sent with request. No response, no business.

​This is pilot episode 1. ​This particular episode do not contain any valuable question nor answer. Every next episode will cover answer to some useful information for bikers, and not only, who are planning to come to ride and/or travel in India.

To understand Rupee value you can use those online converters for EUR and USD.
First place where you can exchange your cash is airport off course. But exchange rate there is the worst. In Bangalore is not a problem to find other places. Be ready to show your documents. ATM is also outside Airport (may be inside too, but I do not remember because didn't need it).
ATMs are not a problem in South India. In big cities they are everywhere, in small towns you can find one or few ATMs anyway. Card payments are acceptable in most places except in small ones, markets, villages, roadside shops etc. Well, you can face a problem if shop of hotel have card terminal connected to some "small/unpopular" Indian bank - they can not use foreign cards, but is is not too common issue. I saw few places where owners do charge 6% more from foreign cards, but not because they are greedy - bank just charge 6% extra as commission from non domestic cards.
I had a problem once when was long official holidays and in small town all ATMs were "empty", but it happened only once. 
There is also one option to get cash. For example Hampi (I was there7 times) You can get cash in Travel Agency. They will swipe your card and give you cash with deducted commission. "Exchange rate" wasn't great, but this was only option to get cash there or go 16 km to closes town Hospet.
I might be a bit confusing for you - here rotating old and new banknotes. 500 and 1000 Rupee banknotes are withdrawn from circulation after last money reformation. So, If somebody try to give you it as change - it is brutal cheating. Here also circulate many different design 1, 2, 5 Rupees coins. We have also 10 Rupees coins, but they are not "popular" in villages and small towns because "peasants" think that they are not legal or fake or whatever is in they mind.