trying to get something cheap is usually a recipe for spending more money in the long run.
You can get a garmin car sat nav for about 100 quid, while a motorcycle ones start at about 300. As mentioned above, the car ones are not waterproof, vibration proof or dustproof. You could theoretically carry one in your tank bag, but it will be hard to read since it will be too low and hard to read because it will be behind the shiny reflective plastic that is the tank bag cover. If you really want to do it cheap then do it that way.
But in the end you will eventually buy a motorcycle unit and have spent more money than if you had bought a motorcycle unit in the first place.
Similarly ... there are brands that are cheaper than Garmin. In fact most brands are cheaper than Garmin. You could buy those to save money. But then you have to buy maps. Most free maps only work with Garmin units.
So in the end you have to buy an expensive brand and the expensive motorcycle units.
The smartest way I would recommend for you to save money on a GPS is .. some shops on the internet sell reconditioned garmin units. Handtec.co.uk is one of them. Usually they are Garmin units that had faults, got returned and exchanged for a new one, and have been factory reconditioned by Garmin themselves. These reconditioned units come with guarantees and are often 30% - 50% cheaper than "brand new".
Here's one I would recommend ... A fully reconditioned Zumo 400 for GBP 202.