I just use a socket the same size as the bearing to tap it in with a hammer, making sure it goes in square. You shouldn't need to do anything special like freeze it.

Bearing was very very tight and sadly the gentle tap with the hammer kept getter harder and harder until bearing is now squashed

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1969 Cooper "S"
1967 Mini Deluxe
1973 Clubman Van (the fleet spare)
1978 ex 1275 LS ("Wizard" Eaton Supercharged)
2015 HSV GenF GTS(occasional drive & tow car)
2019 MINI F55 Cooper S

Michael,
Tap it in square and flush with an idler gear and a brass dolly. This supports the bearing and you can see if it's going in square.
THEN, use a socket to tap it just below flush.

[edit] I now use the same method to fit the other idler bearing to the gearcase. I used to use a couple of sockets, nuts and some M12 threaded rod (which I use for removal), but it's too easy to start the bearing in crooked.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

For what its worth Sommerford sell the correct bearing remover Part No 18G617C. Bit pricy at 83.40 GBP . I bought one - one of the best specialised mini tools I have

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Mk1 Cooper S
Mini K Rally car

Best $67 spent on ebay ...! Made it easy.

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1970 Mk2 Cooper S under restoration

I made a split collet tool to remove the idler gear bearing. Details in the how to forum.
Also does front top arm needle bearings.
Another bigger one does rear suspension arm needle bearings.
[Edit] which are a right bastard to remove without a puller.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

Yes Dr, saw all you great work in the how to forum a while ago. I don't have a lathe, so this was the best option. I did though make a puller for the outrigger bearing from 40x40 rhs.

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1970 Mk2 Cooper S under restoration

These are the Churchill bearing extractors for idler gear (on left) and spigot bearings in the transfer housing.
After damaging a transfer housing, I decided to invest in the correct service tools and ordered them from Brooklands auto parts. Took 6 months for delivery and at $39.66 each in 1978, in today's money with inflation and compound interest considered, that's why I'm not a millionaire....
But like crisonic says, very useful when you need it.

This discussion got me thinking, over the years I have tried a few methods to remove a clutch housing Torrington bearing. Have run a bead of weld around the bearing, that worked but I was concerned about too much heat. Tried a small 3 pronged bearing puller but this ended up by destroying the bearing and making the job more difficult. Having a few spare housings with bearings intact I thought I'd have a go at Doc's "How to".
Spent some time this afternoon turning up the collets as in the Doc’s write up. Don’t have a milling machine, just used a power hacksaw to cut a 5mm slot in the collet body forming 2 halves then followed the rest of Doc's steps. Tested the device and removed a bearing with little effort.
Excellent "How to", thanks Doc.

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Clive G
1969 Mk II Cooper S
1970 MK II Cooper S
1963 Triumph Spitfire
1982 RX-7 Series 2

I thought that looked familiar!

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.