Converting from BECMI movement stats to D&D 5e Speed stats starts with looking at what the numbers in each are like, and then making sure they're converted in a way that recognises that playability is the goal rather than something mathematically pure (though if we can have both, great).
A comparison of movement rates in BECMI and D&D 5e
If you survey the per-round move* and Speed statistics in BECMI and 5e, you'll see there's a much wider range of ground speeds in BECMI than in 5e: the benchmark (human PC standard) in BECMI is 40' and ranges from a high of 70' (a panther) to lows of 3' (a giant bat, gray ooze, or shrieker) and even 1' (a green slime; considered a mere trap in 5e). D&D 5e has a much more compressed range of ground speeds, with Speed 30 ft. as the human benchmark, and the MM showing a range from Speed 60 ft. at the high end (various; for examples, an allosaurus or a skeletal horse) to Speed 5 ft. at the low end† (a grounded bat).
This gives us two scales, one wider and one more compressed, each with slightly different middle values (40 vs. 30). A straight conversion is the first thing that might seem obvious, but some details from the survey should give pause. Comparing some monsters directly shows us that there isn't a straight conversion rate that would make conversions match up for monsters that are in both. For example, we can compare a gray ooze and a bat in each. A gray ooze in 5e is an okay Speed 10 ft., not the slowest thing in the game, while a BECMI gray ooze is a glacial 3'… but this makes a bat faster on its feet than the ooze in BECMI (move 10') while in 5e the bat's Speed 5 ft. is slower than the ooze.
That doesn't mean that a conversion factor isn't possible, but it does mean that any conversion method used on BECMI monster move rates will give results that don't quite fit the rates that D&D 5e monsters have been assigned.
Fortunately, what that means is that some ideal of accuracy isn't quite achievable, so something approximate is the best possible, and is going to have to be good enough to be playable.
A rough conversion
A rough and ready conversion is just to knock off 10' from BECMI move stats for anything 40' and up, giving a range from Speed 60 ft. to Speed 30 ft. Then for move 30' to 10', knock 5 off BECMI move stats for a range from Speed 25 ft. to Speed 5 ft. Anything lower, just set it to Speed 5 ft. and move on.
This has the advantage that human-speed opponents in BECMI end up with Speed 30 ft. in 5e, and the slightly-less-than-human-speed opponents in BECMI end up with Speed 25 ft., which is what D&D 5e assigns to those two classes of opponents. These make up a large proportion of BECMI monsters, so having the categories match up like that is nice.
It also means that you can use BECMI monsters on or off a grid as readily as native 5e monsters.
An alternative, simpler option to consider: no conversion
It's not entirely unreasonable to just use the BECMI per-round speed directly as a D&D 5e Speed. Most monsters have either 40' or 30' of movement, which is as much or a bit more than the typical 5e adventurer.
If you're planning on using exclusively BECMI monsters, then these slightly higher speeds can just be part of the reality that the adventurers have to deal with.
* The number in parens is the per-round move; e.g., 90' (30') is a creature that can move 30' during a combat round. The first number isn't used in combat, so we can ignore it.
† This low excludes monsters with a Speed 0 ft. rating to indicate monsters that are either immobile or which can only use some other movement mode such as flight; in BECMI, these monsters simply have no (ground) move statistic at all.