Mycelium probably takes the highest fee possible and applies that. Bitcoin Core is much better because it has more refined options to fine-tune your fee. I never used Mycelium but I guess it has just "cheap-normal-fast" type of options, very limited.
Unless you can find a solution within Mycelium then you are most likely stuck with what you have. All wallets should have the same system of fees than Bitcoin Core, it is really the best out there.
They actually released an update a few weeks ago implementing a more flexible Fee selector. Now you can choose between a bunch of fee options that vary from 0 sat/byte up to 303 sat/byte.
Also, you are recommending a "full node" wallet for PC to someone who is using a SPV mobile wallet. Not really the same thing.
The miner picker update is really helpful guess they heard what people demands. Now you can do a 10Ksats/kb for huge sized transactions and have viabtc to confirm it
Can I change this bumping to different price somehow?
Because I see option only 0.001 and it is quite a lot! About 5.96$.
Can someone explain to me what is this bump fee because i haven't seen it on mycelium yet. Is it a rbf?
Have you updated your app op? as miner fees are much more flexible now. If you've got a stuck transaction/s its better to post the TXID/s here.