Software is typically much cheaper and has more functionality as well. You are tied to the computer but if you need to be mobile (like recording in a rehersal space) just get a laptop.
Since you are familiar with the old tape 4-track proicess, there are still machines like that out there and dollar for dollar they are stupid cheap. Tascam sells
Invalid Link Removed that costs $650, less than what I paid for one of their cassette 4-tracks back in the 1980s.
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Zoom makes similar machines, the current R20 for $450 has 16 tracks, an onboard drum machine and an onboard synth that can be played by plugging in a MIDI keyboard
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You can buy even less expensive machines with fewer tracks, here's a $300 Tascam with 8 tracks.
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They all come with onboard effects and have a DI input for your bass or other electric instruments.
Some handheld recorders can multitrack, too. For instance, the Zoom H6 which is a 6 track (doh) machine for $280.
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You can buy older, discontinued machines for even less. I have a Boss 8-track from about 15 years ago that I don't use. It's similar to that Tascam 8-track above except on the used market it's only worth maybe $100 max. Plus it has a CD-R burner for backups or burning playable CDs, something more recent machines can't do.
Like I wrote, software is cheaper (free, even) than a hardware recorder if you ignore the money you spent on the computer or tablet. You can buy audio interaces for under $100 and they all come with recording software. Then you just need a mike (if you plan on singing or miking up instruments or amps) and some headphones. You can plug your bass into the interface without needing a DI. The free software is usually track limited (8 tracks being common) with a path to buy the "full" version later at a discount. If you happen to own an Apple, you get Garageband for free which is even more fully featured than the free "lite" packages that come with interfaces.